Least Common Multiple of 32 and 51

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 32 and 51 the smallest integer that is 1632 that is divisible by both numbers.

Least Common Multiple (LCM) of 32 and 51 is 1632.

LCM(32,51) = 1632

LCM of 32 and 51

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

LCM of:
and

Least Common Multiple of 32 and 51

LCM of 32 and 51 is 1632

Least common multiple can be found by multiplying the highest exponent prime factors of 32 and 51. First we will calculate the prime factors of 32 and 51.

Prime Factorization of 32


2 32
2 16
2 8
2 4
2 2
1

Prime factors of 32 are 2. Prime factorization of 32 in exponential form is:

32 = 25

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

Now multiplying the highest exponent prime factors to calculate the LCM of 32 and 51.

LCM(32,51) = 25×31×171
LCM(32,51) = 1632

Factors of 32

List of positive integer factors of 32 that divides 32 without a remainder.

1, 2, 4, 8, 16, 32

Factors of 51

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

1, 3, 17, 51

Least Common Multiple of 32 and 51 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 32 and 51, than apply into the LCM equation.

GCF(32,51) = 1
LCM(32,51) = ( 32 × 51) / 1
LCM(32,51) = 1632 / 1
LCM(32,51) = 1632

Properties of LCM 32 and 51

(i) The LCM of 51 and 32 is associative

LCM of 32 and 51 = LCM of 51 and 32

Related Least Common Multiples of 32

Related Least Common Multiples of 51

Frequently Asked Questions on LCM of 32 and 51

1. What is the LCM of 32 and 51?

Answer: LCM of 32 and 51 is 1632.

2. What are the Factors of 32?

Answer: Factors of 32 are 1, 2, 4, 8, 16, 32. There are 6 integers that are factors of 32. The greatest factor of 32 is 32.

3. 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.

4. How to Find the LCM of 32 and 51?

Answer:

Least Common Multiple of 32 and 51 = 1632

Step 1: Find the prime factorization of 32

32 = 2 x 2 x 2 x 2 x 2

Step 2: Find the prime factorization of 51

51 = 3 x 17

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

LCM = 1632 = 2 x 2 x 2 x 2 x 2 x 3 x 17

Step 4: Therefore, the least common multiple of 32 and 51 is 1632.