Least Common Multiple of 32 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 32 and 52 the smallest integer that is 416 that is divisible by both numbers.

Least Common Multiple (LCM) of 32 and 52 is 416.

LCM(32,52) = 416

LCM of 32 and 52

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

LCM of:
and

Least Common Multiple of 32 and 52

LCM of 32 and 52 is 416

Least common multiple can be found by multiplying the highest exponent prime factors of 32 and 52. First we will calculate the prime factors of 32 and 52.

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 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 32 and 52.

LCM(32,52) = 25×131
LCM(32,52) = 416

Factors of 32

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

1, 2, 4, 8, 16, 32

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 32 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 32 and 52, than apply into the LCM equation.

GCF(32,52) = 4
LCM(32,52) = ( 32 × 52) / 4
LCM(32,52) = 1664 / 4
LCM(32,52) = 416

Properties of LCM 32 and 52

(i) The LCM of 52 and 32 is associative

LCM of 32 and 52 = LCM of 52 and 32

Related Least Common Multiples of 32

Related Least Common Multiples of 52

Frequently Asked Questions on LCM of 32 and 52

1. What is the LCM of 32 and 52?

Answer: LCM of 32 and 52 is 416.

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 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 32 and 52?

Answer:

Least Common Multiple of 32 and 52 = 416

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 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 = 416 = 2 x 2 x 2 x 2 x 2 x 13

Step 4: Therefore, the least common multiple of 32 and 52 is 416.