LCM of 15 and 20 is the smallest number among all common multiples of 15 and 20. The first few multiples of 15 and 20 are (15, 30, 45, 60, 75, 90, 105, . . . ) and (20, 40, 60, 80, 100, 120, . . . ) respectively. There are 3 commonly used methods to find LCM of 15 and 20 - by division method, by prime factorization, and by listing multiples.

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1.LCM of 15 and 20
2.List of Methods
3.Solved Examples
4.FAQs

Answer: LCM of 15 and 20 is 60.

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Explanation:

The LCM of two non-zero integers, x(15) and y(20), is the smallest positive integer m(60) that is divisible by both x(15) and y(20) without any remainder.


The methods to find the LCM of 15 and 20 are explained below.

By Prime Factorization MethodBy Division MethodBy Listing Multiples

LCM of 15 and 20 by Prime Factorization

Prime factorization of 15 and 20 is (3 × 5) = 31 × 51 and (2 × 2 × 5) = 22 × 51 respectively. LCM of 15 and 20 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 22 × 31 × 51 = 60.Hence, the LCM of 15 and 20 by prime factorization is 60.

LCM of 15 and 20 by Division Method

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To calculate the LCM of 15 and 20 by the division method, we will divide the numbers(15, 20) by their prime factors (preferably common). The product of these divisors gives the LCM of 15 and 20.

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

The LCM of 15 and 20 is the product of all prime numbers on the left, i.e. LCM(15, 20) by division method = 2 × 2 × 3 × 5 = 60.

LCM of 15 and 20 by Listing Multiples

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To calculate the LCM of 15 and 20 by listing out the common multiples, we can follow the given below steps:

Step 1: List a few multiples of 15 (15, 30, 45, 60, 75, 90, 105, . . . ) and 20 (20, 40, 60, 80, 100, 120, . . . . )Step 2: The common multiples from the multiples of 15 and 20 are 60, 120, . . .Step 3: The smallest common multiple of 15 and 20 is 60.

∴ The least common multiple of 15 and 20 = 60.

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FAQs on LCM of 15 and 20

What is the LCM of 15 and 20?

The LCM of 15 and 20 is 60. To find the LCM (least common multiple) of 15 and 20, we need to find the multiples of 15 and 20 (multiples of 15 = 15, 30, 45, 60; multiples of 20 = 20, 40, 60, 80) and choose the smallest multiple that is exactly divisible by 15 and 20, i.e., 60.

Which of the following is the LCM of 15 and 20? 25, 18, 35, 60

The value of LCM of 15, 20 is the smallest common multiple of 15 and 20. The number satisfying the given condition is 60.

If the LCM of 20 and 15 is 60, Find its GCF.

LCM(20, 15) × GCF(20, 15) = 20 × 15Since the LCM of 20 and 15 = 60⇒ 60 × GCF(20, 15) = 300Therefore, the greatest common factor (GCF) = 300/60 = 5.

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What is the Relation Between GCF and LCM of 15, 20?

The following equation can be used to express the relation between GCF and LCM of 15 and 20, i.e. GCF × LCM = 15 × 20.

What are the Methods to Find LCM of 15 and 20?

The commonly used methods to find the LCM of 15 and 20 are: