Least Common Multiple of 51 and 52

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 51 and 52 the smallest integer that is 2652 that is divisible by both numbers.

Least Common Multiple (LCM) of 51 and 52 is 2652.

LCM(51,52) = 2652

LCM of 51 and 52

Least common multiple or lowest common denominator (LCD) can be calculated in three ways;

LCM of:
and

Least Common Multiple of 51 and 52

LCM of 51 and 52 is 2652

Least common multiple can be found by multiplying the highest exponent prime factors of 51 and 52. First we will calculate the prime factors of 51 and 52.

Prime Factorization of 51


3 51
17 17
1

Prime factors of 51 are 3,17. Prime factorization of 51 in exponential form is:

51 = 31×171

Prime Factorization of 52


2 52
2 26
13 13
1

Prime factors of 52 are 2,13. Prime factorization of 52 in exponential form is:

52 = 22×131

Now multiplying the highest exponent prime factors to calculate the LCM of 51 and 52.

LCM(51,52) = 22×31×131×171
LCM(51,52) = 2652

Factors of 51

List of positive integer factors of 51 that divides 51 without a remainder.

1, 3, 17, 51

Factors of 52

List of positive integer factors of 52 that divides 52 without a remainder.

1, 2, 4, 13, 26, 52

Least Common Multiple of 51 and 52 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 51 and 52, than apply into the LCM equation.

GCF(51,52) = 1
LCM(51,52) = ( 51 × 52) / 1
LCM(51,52) = 2652 / 1
LCM(51,52) = 2652

Properties of LCM 51 and 52

(i) The LCM of 52 and 51 is associative

LCM of 51 and 52 = LCM of 52 and 51

Related Least Common Multiples of 51

Related Least Common Multiples of 52

Frequently Asked Questions on LCM of 51 and 52

1. What is the LCM of 51 and 52?

Answer: LCM of 51 and 52 is 2652.

2. What are the Factors of 51?

Answer: Factors of 51 are 1, 3, 17, 51. There are 4 integers that are factors of 51. The greatest factor of 51 is 51.

3. What are the Factors of 52?

Answer: Factors of 52 are 1, 2, 4, 13, 26, 52. There are 6 integers that are factors of 52. The greatest factor of 52 is 52.

4. How to Find the LCM of 51 and 52?

Answer:

Least Common Multiple of 51 and 52 = 2652

Step 1: Find the prime factorization of 51

51 = 3 x 17

Step 2: Find the prime factorization of 52

52 = 2 x 2 x 13

Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:

LCM = 2652 = 2 x 2 x 3 x 13 x 17

Step 4: Therefore, the least common multiple of 51 and 52 is 2652.