LCM of 15 and 60

LCM of 15 and 60 is 60. It is vital to follow the best study source for effective learning of concepts. For this purpose, expert teachers prepared the article Prime Factorisation and Division Method for LCM and HCF to ensure a proper understanding of concepts. In this article, students can learn the detailed format of how to find the LCM and HCF of given numbers in a precise manner. Let us learn how to find the least common multiple of 15 and 60, along with solved examples and FAQs using simple steps here.

What is LCM of 15 and 60?

The Least Common Multiple of 15 and 60 is 60.

lcm of 15 and 60

How to Find LCM of 15 and 60?

The below methods are used to find the LCM of 15 and 60:

  • Prime Factorisation
  • Division method
  • Listing the multiples

LCM of 15 and 60 Using Prime Factorisation Method

By prime factorisation method, we can write 15 and 60 as the product of prime numbers, such that;

15 = 3 × 5

60 = 2 × 2 × 3 × 5

LCM (15, 60) = 2 × 2 × 3 × 5 = 60

LCM of 15 and 60 Using Division Method

We divide the numbers 15 and 60 by their prime factors until we get the result as one in the complete row to find their LCM in division method. The product of these divisors denotes the least common multiple of 15 and 60.

2 15 60
2 15 30
3 15 15
5 5 5
x 1 1

No more further division can be done.

Hence, LCM (15, 60) = 2 × 2 × 3 × 5 = 60

LCM of 15 and 60 Using Listing the Multiples

In this method, we list out the multiples of 15 and 60 to calculate their LCM. The multiples of 15 and 60 are shown in the below table.

Multiples of 15 Multiples of 60
15 60
30 120
45 180
60 240
75 300
90 360

LCM (15, 60) = 60

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Video Lesson on Applications of LCM

Solved Examples 

Q. 1: The product of two numbers is 900. If their GCD is 15, find their LCM.

Solution: Given,

GCD = 15

Product of numbers = 900

We know that,

LCM × GCD = Product of numbers

LCM = Product of numbers / GCD

LCM = 900 / 15

LCM = 60

Hence, the LCM is 60.

Q. 2: What is the smallest number that is divisible by both 15 and 60?

Solution: 60 is the smallest number that is divisible by both 15 and 60. 

Frequently Asked Questions on LCM of 15 and 60

Q1

What is the LCM of 15 and 60?

The LCM of 15 and 60 is 60.
Q2

What are the common factors of 15 and 60?

The common factors of 15 and 60 are 1, 3, 5 and 15.
Q3

Is the LCM of 15 and 60 the same as the HCF of 15 and 60?

No. The LCM of 15 and 60 is 60 and the HCF of 15 and 60 is 15.
Q4

List the methods used to determine the LCM of 15 and 60.

The following methods are used to determine the LCM of 15 and 60

Prime Factorisation

Division Method

Listing the Multiples

Q5

Give the relation between GCF and LCM of 15 and 60.

The relation between GCF and LCM of 15 and 60 is

GCF × LCM = 15 × 60

GCF × LCM = 900

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