LCM of 4 and 7 is the smallest number among all common multiples of 4 and 7. The first few multiples of 4 and 7 are (4, 8, 12, 16, 20, . . . ) and (7, 14, 21, 28, 35, . . . ) respectively. There are 3 commonly used methods to find LCM of 4 and 7 - by division method, by listing multiples, and by prime factorization.

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1.LCM of 4 and 7
2.List of Methods
3.Solved Examples
4.FAQs

Answer: LCM of 4 and 7 is 28.

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Explanation:

The LCM of two non-zero integers, x(4) and y(7), is the smallest positive integer m(28) that is divisible by both x(4) and y(7) without any remainder.


Let's look at the different methods for finding the LCM of 4 and 7.

By Prime Factorization MethodBy Listing MultiplesBy Division Method

LCM of 4 and 7 by Prime Factorization

Prime factorization of 4 and 7 is (2 × 2) = 22 and (7) = 71 respectively. LCM of 4 and 7 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 22 × 71 = 28.Hence, the LCM of 4 and 7 by prime factorization is 28.

LCM of 4 and 7 by Listing Multiples

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To calculate the LCM of 4 and 7 by listing out the common multiples, we can follow the given below steps:

Step 1: List a few multiples of 4 (4, 8, 12, 16, 20, . . . ) and 7 (7, 14, 21, 28, 35, . . . . )Step 2: The common multiples from the multiples of 4 and 7 are 28, 56, . . .Step 3: The smallest common multiple of 4 and 7 is 28.

∴ The least common multiple of 4 and 7 = 28.

LCM of 4 and 7 by Division Method

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To calculate the LCM of 4 and 7 by the division method, we will divide the numbers(4, 7) by their prime factors (preferably common). The product of these divisors gives the LCM of 4 and 7.

Step 3: Continue the steps until only 1s are left in the last row.

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The LCM of 4 and 7 is the product of all prime numbers on the left, i.e. LCM(4, 7) by division method = 2 × 2 × 7 = 28.