LCM of 15 and 30 is the smallest number among all common multiples of 15 and 30. The first few multiples of 15 and 30 are (15, 30, 45, 60, 75, 90, . . . ) and (30, 60, 90, 120, 150, 180, 210, . . . ) respectively. There are 3 commonly used methods to find LCM of 15 and 30 - by listing multiples, by prime factorization, and by division method.

You are watching: What is the least common multiple of 15 and 30

1.LCM of 15 and 30
2.List of Methods
3.Solved Examples
4.FAQs

Answer: LCM of 15 and 30 is 30.

*

Explanation:

The LCM of two non-zero integers, x(15) and y(30), is the smallest positive integer m(30) that is divisible by both x(15) and y(30) without any remainder.


The methods to find the LCM of 15 and 30 are explained below.

By Prime Factorization MethodBy Listing MultiplesBy Division Method

LCM of 15 and 30 by Prime Factorization

Prime factorization of 15 and 30 is (3 × 5) = 31 × 51 and (2 × 3 × 5) = 21 × 31 × 51 respectively. LCM of 15 and 30 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 21 × 31 × 51 = 30.Hence, the LCM of 15 and 30 by prime factorization is 30.

LCM of 15 and 30 by Listing Multiples

*

To calculate the LCM of 15 and 30 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, . . . ) and 30 (30, 60, 90, 120, 150, 180, 210, . . . . )Step 2: The common multiples from the multiples of 15 and 30 are 30, 60, . . .Step 3: The smallest common multiple of 15 and 30 is 30.

∴ The least common multiple of 15 and 30 = 30.

LCM of 15 and 30 by Division Method

*

To calculate the LCM of 15 and 30 by the division method, we will divide the numbers(15, 30) by their prime factors (preferably common). The product of these divisors gives the LCM of 15 and 30.

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

The LCM of 15 and 30 is the product of all prime numbers on the left, i.e. LCM(15, 30) by division method = 2 × 3 × 5 = 30.

☛ Also Check:


*


FAQs on LCM of 15 and 30

What is the LCM of 15 and 30?

The LCM of 15 and 30 is 30. To find the LCM (least common multiple) of 15 and 30, we need to find the multiples of 15 and 30 (multiples of 15 = 15, 30, 45, 60; multiples of 30 = 30, 60, 90, 120) and choose the smallest multiple that is exactly divisible by 15 and 30, i.e., 30.

If the LCM of 30 and 15 is 30, Find its GCF.

LCM(30, 15) × GCF(30, 15) = 30 × 15Since the LCM of 30 and 15 = 30⇒ 30 × GCF(30, 15) = 450Therefore, the greatest common factor = 450/30 = 15.

What is the Least Perfect Square Divisible by 15 and 30?

The least number divisible by 15 and 30 = LCM(15, 30)LCM of 15 and 30 = 2 × 3 × 5 ⇒ Least perfect square divisible by each 15 and 30 = LCM(15, 30) × 2 × 3 × 5 = 900 Therefore, 900 is the required number.

How to Find the LCM of 15 and 30 by Prime Factorization?

To find the LCM of 15 and 30 using prime factorization, we will find the prime factors, (15 = 3 × 5) and (30 = 2 × 3 × 5). LCM of 15 and 30 is the product of prime factors raised to their respective highest exponent among the numbers 15 and 30.⇒ LCM of 15, 30 = 21 × 31 × 51 = 30.

See more: What Part Of Turkey Is Called Turkey Knuckles, 7 Turkey Knuckles Ideas

What is the Relation Between GCF and LCM of 15, 30?

The following equation can be used to express the relation between GCF and LCM of 15 and 30, i.e. GCF × LCM = 15 × 30.