LCM of 10, 25, 35, and 40
LCM of 10, 25, 35, and 40 is the smallest number among all common multiples of 10, 25, 35, and 40. The first few multiples of 10, 25, 35, and 40 are (10, 20, 30, 40, 50 . . .), (25, 50, 75, 100, 125 . . .), (35, 70, 105, 140, 175 . . .), and (40, 80, 120, 160, 200 . . .) respectively. There are 3 commonly used methods to find LCM of 10, 25, 35, 40  by prime factorization, by division method, and by listing multiples.
1.  LCM of 10, 25, 35, and 40 
2.  List of Methods 
3.  Solved Examples 
4.  FAQs 
What is the LCM of 10, 25, 35, and 40?
Answer: LCM of 10, 25, 35, and 40 is 1400.
Explanation:
The LCM of four nonzero integers, a(10), b(25), c(35), and d(40), is the smallest positive integer m(1400) that is divisible by a(10), b(25), c(35), and d(40) without any remainder.
Methods to Find LCM of 10, 25, 35, and 40
The methods to find the LCM of 10, 25, 35, and 40 are explained below.
 By Listing Multiples
 By Prime Factorization Method
 By Division Method
LCM of 10, 25, 35, and 40 by Listing Multiples
To calculate the LCM of 10, 25, 35, 40 by listing out the common multiples, we can follow the given below steps:
 Step 1: List a few multiples of 10 (10, 20, 30, 40, 50 . . .), 25 (25, 50, 75, 100, 125 . . .), 35 (35, 70, 105, 140, 175 . . .), and 40 (40, 80, 120, 160, 200 . . .).
 Step 2: The common multiples from the multiples of 10, 25, 35, and 40 are 1400, 2800, . . .
 Step 3: The smallest common multiple of 10, 25, 35, and 40 is 1400.
∴ The least common multiple of 10, 25, 35, and 40 = 1400.
LCM of 10, 25, 35, and 40 by Prime Factorization
Prime factorization of 10, 25, 35, and 40 is (2 × 5) = 2^{1} × 5^{1}, (5 × 5) = 5^{2}, (5 × 7) = 5^{1} × 7^{1}, and (2 × 2 × 2 × 5) = 2^{3} × 5^{1} respectively. LCM of 10, 25, 35, and 40 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2^{3} × 5^{2} × 7^{1} = 1400.
Hence, the LCM of 10, 25, 35, and 40 by prime factorization is 1400.
LCM of 10, 25, 35, and 40 by Division Method
To calculate the LCM of 10, 25, 35, and 40 by the division method, we will divide the numbers(10, 25, 35, 40) by their prime factors (preferably common). The product of these divisors gives the LCM of 10, 25, 35, and 40.
 Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 10, 25, 35, and 40. Write this prime number(2) on the left of the given numbers(10, 25, 35, and 40), separated as per the ladder arrangement.
 Step 2: If any of the given numbers (10, 25, 35, 40) is a multiple of 2, divide it by 2 and write the quotient below it. Bring down any number that is not divisible by the prime number.
 Step 3: Continue the steps until only 1s are left in the last row.
The LCM of 10, 25, 35, and 40 is the product of all prime numbers on the left, i.e. LCM(10, 25, 35, 40) by division method = 2 × 2 × 2 × 5 × 5 × 7 = 1400.
ā Also Check:
 LCM of 7, 14 and 21  42
 LCM of 24 and 64  192
 LCM of 850 and 680  3400
 LCM of 5 and 8  40
 LCM of 40, 56 and 60  840
 LCM of 20, 25 and 30  300
 LCM of 21 and 22  462
LCM of 10, 25, 35, and 40 Examples

Example 1: Find the smallest number which when divided by 10, 25, 35, and 40 leaves 4 as the remainder in each case.
Solution:
The smallest number exactly divisible by 10, 25, 35, and 40 = LCM(10, 25, 35, 40) ⇒ Smallest number which leaves 4 as remainder when divided by 10, 25, 35, and 40 = LCM(10, 25, 35, 40) + 4
 10 = 2^{1} × 5^{1}
 25 = 5^{2}
 35 = 5^{1} × 7^{1}
 40 = 2^{3} × 5^{1}
LCM(10, 25, 35, 40) = 2^{3} × 5^{2} × 7^{1} = 1400
⇒ The required number = 1400 + 4 = 1404. 
Example 2: Which of the following is the LCM of 10, 25, 35, 40? 36, 1400, 24, 120.
Solution:
The value of LCM of 10, 25, 35, and 40 is the smallest common multiple of 10, 25, 35, and 40. The number satisfying the given condition is 1400. ∴LCM(10, 25, 35, 40) = 1400.

Example 3: Find the smallest number that is divisible by 10, 25, 35, 40 exactly.
Solution:
The value of LCM(10, 25, 35, 40) will be the smallest number that is exactly divisible by 10, 25, 35, and 40.
⇒ Multiples of 10, 25, 35, and 40: Multiples of 10 = 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, . . . ., 1360, 1370, 1380, 1390, 1400, . . . .
 Multiples of 25 = 25, 50, 75, 100, 125, 150, 175, 200, 225, 250, . . . ., 1300, 1325, 1350, 1375, 1400, . . . .
 Multiples of 35 = 35, 70, 105, 140, 175, 210, 245, 280, 315, 350, . . . ., 1260, 1295, 1330, 1365, 1400, . . . .
 Multiples of 40 = 40, 80, 120, 160, 200, 240, 280, 320, 360, 400, . . . ., 1320, 1360, 1400, . . . .
Therefore, the LCM of 10, 25, 35, and 40 is 1400.
FAQs on LCM of 10, 25, 35, and 40
What is the LCM of 10, 25, 35, and 40?
The LCM of 10, 25, 35, and 40 is 1400. To find the least common multiple of 10, 25, 35, and 40, we need to find the multiples of 10, 25, 35, and 40 (multiples of 10 = 10, 20, 30, 40 . . . . 1400 . . . . ; multiples of 25 = 25, 50, 75, 100 . . . . 1400 . . . . ; multiples of 35 = 35, 70, 105, 140 . . . . 1400 . . . . ; multiples of 40 = 40, 80, 120, 160 . . . . 1400 . . . . ) and choose the smallest multiple that is exactly divisible by 10, 25, 35, and 40, i.e., 1400.
What is the Least Perfect Square Divisible by 10, 25, 35, and 40?
The least number divisible by 10, 25, 35, and 40 = LCM(10, 25, 35, 40)
LCM of 10, 25, 35, and 40 = 2 × 2 × 2 × 5 × 5 × 7 [Incomplete pair(s): 2, 7]
⇒ Least perfect square divisible by each 10, 25, 35, and 40 = LCM(10, 25, 35, 40) × 2 × 7 = 19600 [Square root of 19600 = √19600 = ±140]
Therefore, 19600 is the required number.
Which of the following is the LCM of 10, 25, 35, and 40? 32, 1400, 2, 50
The value of LCM of 10, 25, 35, 40 is the smallest common multiple of 10, 25, 35, and 40. The number satisfying the given condition is 1400.
How to Find the LCM of 10, 25, 35, and 40 by Prime Factorization?
To find the LCM of 10, 25, 35, and 40 using prime factorization, we will find the prime factors, (10 = 2^{1} × 5^{1}), (25 = 5^{2}), (35 = 5^{1} × 7^{1}), and (40 = 2^{3} × 5^{1}). LCM of 10, 25, 35, and 40 is the product of prime factors raised to their respective highest exponent among the numbers 10, 25, 35, and 40.
⇒ LCM of 10, 25, 35, 40 = 2^{3} × 5^{2} × 7^{1} = 1400.
visual curriculum