LCM of 16 and 17 is 272. LCM denotes the smallest positive number which is a multiple of two or more numbers. For accurate answers to all the questions on the LCM concept, students can refer to the resources designed by the experts anytime, free of cost. LCM with Examples is the best reference guide to enhance the knowledge of the LCM concept among students. Here, we will learn how to find the least common multiple of 16 and 17 with the help of solved examples and FAQs.
What is LCM of 16 and 17?
The answer to this question is 272.
How to Find LCM of 16 and 17?
LCM of 16 and 17 can be determined by using three methods:
- Prime Factorisation
- Division method
- Listing the Multiples
LCM of 16 and 17 Using Prime Factorisation Method
In the prime factorisation method, the given natural numbers are expressed as the product of prime factors. Hence, the numbers 16 and 17 can be expressed as;
16 = 2 × 2 × 2 × 2
17 = 17
LCM (16, 17) = 2 × 2 × 2 × 2 × 17 = 272
LCM of 16 and 17 Using Division Method
In this method, we divide the numbers 16 and 17 by a common prime number until the remainder is a prime number or one. The product of these divisors depicts the least common multiple of 16 and 17.
| 2 | 16 | 17 |
| 2 | 8 | 17 |
| 2 | 4 | 17 |
| 2 | 2 | 17 |
| 17 | 1 | 17 |
| x | 1 | 1 |
No further division can be done.
Hence, LCM (16, 17) = 2 × 2 × 2 × 2 × 17 = 272
LCM of 16 and 17 Using Listing the Multiples
In this method, we list down the multiples of given natural numbers to find the lowest common multiple among them. The following are the few multiples of 16 and 17.
Multiples of 16: 16, 32, 48, 64, 80, 96, 112, 128, 144, 160, …………, 240, 256, 272, …………
Multiples of 17: 17, 34, 51, 68, 85, 102, 119, 136, 153, 170, ……….., 238, 255, 272, ………….
LCM (16, 17) = 272
Related Articles
Prime Factorization and Division Method for LCM and HCF
Video Lesson on Applications of LCM
Solved Examples
1. What is the smallest number that is divisible by both 16 and 17?
Solution: 272 is the smallest number that is divisible by both 16 and 17.
2. The GCD and LCM of the two numbers are 1 and 272. If one number is 17, what is the other number?
Solution: Let the other number be p.
We know that,
GCD × LCM = 17 × p
p = (GCD × LCM) / 17
p = ( 1 × 272) / 17
p = 16
Hence the other number is 16.
Frequently Asked Questions on LCM of 16 and 17
What is the LCM of 16 and 17?
Is the LCM of 16 and 17 the same as the HCF of 16 and 17?
How to find the LCM of 16 and 17 by prime factorisation?
In the prime factorisation method, the given numbers are expressed as the product of prime factors
16 = 2 × 2 × 2 × 2
17 = 17
LCM (16, 17) = 2 × 2 × 2 × 2 × 17 = 272
Hence, 272 is the LCM of 16 and 17 by prime factorisation
What are the methods used to determine the LCM of 16 and 17?
The methods used to determine the LCM of 16 and 17 are
Prime Factorisation
Division Method
Listing the Multiples
Find the GCF if the LCM of 16 and 17 is 272.
GCF × LCM = 16 × 17
Given
LCM = 272
GCF × 272 = 16 × 17
GCF = 1
Comments