Least Common Multiple of 250 and 252

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 250 and 252 the smallest integer that is 31500 that is divisible by both numbers.

Least Common Multiple (LCM) of 250 and 252 is 31500.

LCM(250,252) = 31500

LCM of 250 and 252

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

LCM of:
and

Least Common Multiple of 250 and 252

LCM of 250 and 252 is 31500

Least common multiple can be found by multiplying the highest exponent prime factors of 250 and 252. First we will calculate the prime factors of 250 and 252.

Prime Factorization of 250


2 250
5 125
5 25
5 5
1

Prime factors of 250 are 2,5. Prime factorization of 250 in exponential form is:

250 = 21×53

Prime Factorization of 252


2 252
2 126
3 63
3 21
7 7
1

Prime factors of 252 are 2, 3,7. Prime factorization of 252 in exponential form is:

252 = 22×32×71

Now multiplying the highest exponent prime factors to calculate the LCM of 250 and 252.

LCM(250,252) = 22×32×53×71
LCM(250,252) = 31500

Factors of 250

List of positive integer factors of 250 that divides 250 without a remainder.

1, 2, 5, 10, 25, 50, 125, 250

Factors of 252

List of positive integer factors of 252 that divides 252 without a remainder.

1, 2, 3, 4, 6, 7, 9, 12, 14, 18, 21, 28, 36, 42, 63, 84, 126, 252

Least Common Multiple of 250 and 252 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 250 and 252, than apply into the LCM equation.

GCF(250,252) = 2
LCM(250,252) = ( 250 × 252) / 2
LCM(250,252) = 63000 / 2
LCM(250,252) = 31500

Properties of LCM 250 and 252

(i) The LCM of 252 and 250 is associative

LCM of 250 and 252 = LCM of 252 and 250

Related Least Common Multiples of 250

Related Least Common Multiples of 252

Frequently Asked Questions on LCM of 250 and 252

1. What is the LCM of 250 and 252?

Answer: LCM of 250 and 252 is 31500.

2. What are the Factors of 250?

Answer: Factors of 250 are 1, 2, 5, 10, 25, 50, 125, 250. There are 8 integers that are factors of 250. The greatest factor of 250 is 250.

3. What are the Factors of 252?

Answer: Factors of 252 are 1, 2, 3, 4, 6, 7, 9, 12, 14, 18, 21, 28, 36, 42, 63, 84, 126, 252. There are 18 integers that are factors of 252. The greatest factor of 252 is 252.

4. How to Find the LCM of 250 and 252?

Answer:

Least Common Multiple of 250 and 252 = 31500

Step 1: Find the prime factorization of 250

250 = 2 x 5 x 5 x 5

Step 2: Find the prime factorization of 252

252 = 2 x 2 x 3 x 3 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 = 31500 = 2 x 2 x 3 x 3 x 5 x 5 x 5 x 7

Step 4: Therefore, the least common multiple of 250 and 252 is 31500.