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.
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
What is the LCM of 15 and 60?
What are the common factors of 15 and 60?
Is the LCM of 15 and 60 the same as the HCF of 15 and 60?
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
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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