LCM of 8 and 10 is the smallest number among all common multiples of 8 and 10. The first few multiples of 8 and 10 are (8, 16, 24, 32, 40, . . . ) and (10, 20, 30, 40, . . . ) respectively. There are 3 commonly used methods to find LCM of 8 and 10 - by prime factorization, by listing multiples, and by division method.

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1.LCM of 8 and 10
2.List of Methods
3.Solved Examples
4.FAQs

Answer: LCM of 8 and 10 is 40.

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Explanation:

The LCM of two non-zero integers, x(8) and y(10), is the smallest positive integer m(40) that is divisible by both x(8) and y(10) without any remainder.


Let's look at the different methods for finding the LCM of 8 and 10.

By Prime Factorization MethodBy Listing MultiplesBy Division Method

LCM of 8 and 10 by Prime Factorization

Prime factorization of 8 and 10 is (2 × 2 × 2) = 23 and (2 × 5) = 21 × 51 respectively. LCM of 8 and 10 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 23 × 51 = 40.Hence, the LCM of 8 and 10 by prime factorization is 40.

LCM of 8 and 10 by Listing Multiples

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To calculate the LCM of 8 and 10 by listing out the common multiples, we can follow the given below steps:

Step 1: List a few multiples of 8 (8, 16, 24, 32, 40, . . . ) and 10 (10, 20, 30, 40, . . . . )Step 2: The common multiples from the multiples of 8 and 10 are 40, 80, . . .Step 3: The smallest common multiple of 8 and 10 is 40.

∴ The least common multiple of 8 and 10 = 40.

LCM of 8 and 10 by Division Method

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To calculate the LCM of 8 and 10 by the division method, we will divide the numbers(8, 10) by their prime factors (preferably common). The product of these divisors gives the LCM of 8 and 10.

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

The LCM of 8 and 10 is the product of all prime numbers on the left, i.e. LCM(8, 10) by division method = 2 × 2 × 2 × 5 = 40.

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FAQs on LCM of 8 and 10

What is the LCM of 8 and 10?

The LCM of 8 and 10 is 40. To find the least common multiple of 8 and 10, we need to find the multiples of 8 and 10 (multiples of 8 = 8, 16, 24, 32 . . . . 40; multiples of 10 = 10, 20, 30, 40) and choose the smallest multiple that is exactly divisible by 8 and 10, i.e., 40.

What is the Relation Between GCF and LCM of 8, 10?

The following equation can be used to express the relation between GCF and LCM of 8 and 10, i.e. GCF × LCM = 8 × 10.

If the LCM of 10 and 8 is 40, Find its GCF.

LCM(10, 8) × GCF(10, 8) = 10 × 8Since the LCM of 10 and 8 = 40⇒ 40 × GCF(10, 8) = 80Therefore, the greatest common factor (GCF) = 80/40 = 2.

What is the Least Perfect Square Divisible by 8 and 10?

The least number divisible by 8 and 10 = LCM(8, 10)LCM of 8 and 10 = 2 × 2 × 2 × 5 ⇒ Least perfect square divisible by each 8 and 10 = LCM(8, 10) × 2 × 5 = 400 Therefore, 400 is the required number.

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Which of the following is the LCM of 8 and 10? 36, 40, 35, 3

The value of LCM of 8, 10 is the smallest common multiple of 8 and 10. The number satisfying the given condition is 40.