Least Common Multiple of 32 and 38

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 38 the smallest integer that is 608 that is divisible by both numbers.

Least Common Multiple (LCM) of 32 and 38 is 608.

LCM(32,38) = 608

LCM of 32 and 38

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

LCM of:
and

Least Common Multiple of 32 and 38

LCM of 32 and 38 is 608

Least common multiple can be found by multiplying the highest exponent prime factors of 32 and 38. First we will calculate the prime factors of 32 and 38.

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 38


2 38
19 19
1

Prime factors of 38 are 2,19. Prime factorization of 38 in exponential form is:

38 = 21×191

Now multiplying the highest exponent prime factors to calculate the LCM of 32 and 38.

LCM(32,38) = 25×191
LCM(32,38) = 608

Factors of 32

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

1, 2, 4, 8, 16, 32

Factors of 38

List of positive integer factors of 38 that divides 38 without a remainder.

1, 2, 19, 38

Least Common Multiple of 32 and 38 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 38, than apply into the LCM equation.

GCF(32,38) = 2
LCM(32,38) = ( 32 × 38) / 2
LCM(32,38) = 1216 / 2
LCM(32,38) = 608

Properties of LCM 32 and 38

(i) The LCM of 38 and 32 is associative

LCM of 32 and 38 = LCM of 38 and 32

Related Least Common Multiples of 32

Related Least Common Multiples of 38

Frequently Asked Questions on LCM of 32 and 38

1. What is the LCM of 32 and 38?

Answer: LCM of 32 and 38 is 608.

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 38?

Answer: Factors of 38 are 1, 2, 19, 38. There are 4 integers that are factors of 38. The greatest factor of 38 is 38.

4. How to Find the LCM of 32 and 38?

Answer:

Least Common Multiple of 32 and 38 = 608

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 38

38 = 2 x 19

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

LCM = 608 = 2 x 2 x 2 x 2 x 2 x 19

Step 4: Therefore, the least common multiple of 32 and 38 is 608.