LCM of 6 and 16 is 48. LCM is the method to determine the smallest possible multiple of two or more numbers. Experts formulated the article Least Common Multiple (LCM) in a comprehensive manner to make the learning and understanding of the LCM concept an easy task. Students not only gain a thorough knowledge of the LCM concept but also enhance their skills by referring to this article while solving the problems. In this article, we will discuss how to calculate the least common multiple of 6 and 16, along with solved examples and FAQs.
What is LCM of 6 and 16?
The Least Common Multiple of 6 and 16 is 48.
How to Find LCM of 6 and 16?
We can find the LCM of 6 and 16 using the methods given below:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 6 and 16 Using Prime Factorisation Method
Here, we can express the numbers 6 and 16 as the product of prime numbers. Hence 6 and 16 can be expressed as;
6 = 2 × 3
16 = 2 × 2 × 2 × 2
LCM (6, 16) = 2 × 2 × 2 × 2 × 3 = 48
LCM of 6 and 16 Using Division Method
In this method, to determine the LCM of 6 and 16, we divide the numbers 6 and 16 by their prime factors until we get the result as one in the complete row. The product of these divisors represents the least common multiple of 6 and 16.
| 2 | 6 | 16 |
| 2 | 3 | 8 |
| 2 | 3 | 4 |
| 2 | 3 | 2 |
| 3 | 3 | 1 |
| x | 1 | 1 |
No more further division can be done.
Hence, LCM (6, 16) = 2 × 2 × 2 × 2 × 3 = 48
LCM of 6 and 16 Using Listing the Multiples
Here, we list out the multiples of 6 and 16 to identify the least common multiple of 6 and 16. The multiples of 6 and 16 are given in the table mentioned below.
| Multiples of 6 | Multiples of 16 |
| 6 | 16 |
| 12 | 32 |
| 18 | 48 |
| 24 | 64 |
| 30 | 80 |
| 36 | 96 |
| 42 | 112 |
| 48 | 128 |
| 54 | 144 |
LCM (6, 16) = 48
Related Articles
Prime Factorization and Division Method for LCM and HCF
Video Lesson on Applications of LCM
Solved Examples
Q. 1: What is the smallest number that is divisible by both 6 and 16?
Solution: 48 is the smallest number that is divisible by both 6 and 16.
Q. 2: The GCD and LCM of the two numbers are 2 and 48 respectively. If one number is 16, calculate the other number.
Let the other number be z
We know that,
GCD × LCM = 16 × z
z = (GCD × LCM) / 16
z = (2 × 48) / 16
z = 6
Hence the other number is 6.
Frequently Asked Questions on LCM of 6 and 16
What is the LCM of 6 and 16?
Is the LCM of 6 and 16 the same as the HCF of 6 and 16?
45 is the LCM of 6 and 16. True or False.
If the LCM of 6 and 16 is 48. What is the GCF?
LCM × GCF = 6 × 16
Given
LCM = 48
48 × GCF = 6 × 16
GCF = 2
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