Least Common Multiple of 32 and 49

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 49 the smallest integer that is 1568 that is divisible by both numbers.

Least Common Multiple (LCM) of 32 and 49 is 1568.

LCM(32,49) = 1568

LCM of 32 and 49

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

LCM of:
and

Least Common Multiple of 32 and 49

LCM of 32 and 49 is 1568

Least common multiple can be found by multiplying the highest exponent prime factors of 32 and 49. First we will calculate the prime factors of 32 and 49.

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 49


7 49
7 7
1

Prime factors of 49 are 7. Prime factorization of 49 in exponential form is:

49 = 72

Now multiplying the highest exponent prime factors to calculate the LCM of 32 and 49.

LCM(32,49) = 25×72
LCM(32,49) = 1568

Factors of 32

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

1, 2, 4, 8, 16, 32

Factors of 49

List of positive integer factors of 49 that divides 49 without a remainder.

1, 7, 49

Least Common Multiple of 32 and 49 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 49, than apply into the LCM equation.

GCF(32,49) = 1
LCM(32,49) = ( 32 × 49) / 1
LCM(32,49) = 1568 / 1
LCM(32,49) = 1568

Properties of LCM 32 and 49

(i) The LCM of 49 and 32 is associative

LCM of 32 and 49 = LCM of 49 and 32

Related Least Common Multiples of 32

Related Least Common Multiples of 49

Frequently Asked Questions on LCM of 32 and 49

1. What is the LCM of 32 and 49?

Answer: LCM of 32 and 49 is 1568.

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 49?

Answer: Factors of 49 are 1, 7, 49. There are 3 integers that are factors of 49. The greatest factor of 49 is 49.

4. How to Find the LCM of 32 and 49?

Answer:

Least Common Multiple of 32 and 49 = 1568

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 49

49 = 7 x 7

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

LCM = 1568 = 2 x 2 x 2 x 2 x 2 x 7 x 7

Step 4: Therefore, the least common multiple of 32 and 49 is 1568.