LCM of 17 and 51

LCM of 17 and 51 is 51. The number evenly divisible by 17 and 51 gives the LCM value. Least common multiples of 17 and 51 are found by using the common multiples. (17, 34, 51, 68, 85, 102, 119, ….) and (51, 102, 153, 204, 255,….) are the multiples of 17 and 51. The LCM of two numbers with the help of prime factorization, division and by listing the multiples are discussed in a stepwise format here for a better knowledge of fundamental concepts among the students. 

Also read: Least common multiple

What is LCM of 17 and 51?

The answer to this question is 51. The LCM of 17 and 51 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 17 and 51, is the smallest positive integer 51 which is divisible by both 17 and 51 with no remainder.

lcm of 17 and 51

How to Find LCM of 17 and 51?

LCM of 17 and 51 can be found using three methods:

  • Prime Factorisation
  • Division method
  • Listing the multiples

LCM of 17 and 51 Using Prime Factorisation Method

The prime factorisation of 17 and 51, respectively, is given by:

17 = 17 = 5¹

51 = 3 x 17  = 3¹ x 17¹

LCM (17, 51) = 51

LCM of 17 and 51 Using Division Method

We’ll divide the numbers (17, 51) by their prime factors to get the LCM of 17 and 51 using the division method (preferably common). The LCM of 17 and 51 is calculated by multiplying these divisors.

3

17

51

17

17

17

x

1

1

No further division can be done. 

Hence, LCM (17, 51) = 51

LCM of 17 and 51 Using Listing the Multiples

To calculate the LCM of 17 and 51 by listing out the common multiples, list the multiples as shown below

Multiples of 17

Multiples of 51

17

51

34

102

51

153

68

204

LCM (17, 51) = 51

Related Articles

Video Lesson on Applications of LCM

LCM of 17 and 51 Solved Examples 

Question: What is the smallest number which is exactly divisible by 17 and 51?

Solution:

We know that

The smallest number which is exactly divisible by 17 and 51 is the LCM.

Multiples of 17 = 17, 34, 51, 68, 85, 102, 119, ….

Multiples of 51 = 51, 102, 153, 204, 255, 306, 357,….

Hence, the LCM of 17 and 51 is 51.

Frequently Asked Questions on LCM of 17 and 51

Q1

What is the LCM of 17 and 51 using the prime factorization method?

To find the LCM using the prime factorization, we should know the prime factors.

17 = 17 = 5¹

51 = 3 x 17 = 3¹ x 17¹

LCM of 17 and 51 is the product of prime factors raised to the highest exponent among the numbers 17 and 51

LCM of 17 and 51 = 51

Q2

If the LCM of 17 and 51 is 51, find the GCF.

LCM x GCF = 17 x 51

Given

LCM of 17 and 51 = 51

51 x GCF = 867

GCF = 867/51 = 17

Q3

Show the relation between GCF and LCM of 17 and 51.

The relation between GCF and LCM of 17 and 51 is

LCM x GCF = 17 x 51

LCM x GCF = 867

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