Least Common Multiple of 252 and 255

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 252 and 255 the smallest integer that is 21420 that is divisible by both numbers.

Least Common Multiple (LCM) of 252 and 255 is 21420.

LCM(252,255) = 21420

LCM of 252 and 255

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

LCM of:
and

Least Common Multiple of 252 and 255

LCM of 252 and 255 is 21420

Least common multiple can be found by multiplying the highest exponent prime factors of 252 and 255. First we will calculate the prime factors of 252 and 255.

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

Prime Factorization of 255


3 255
5 85
17 17
1

Prime factors of 255 are 3, 5,17. Prime factorization of 255 in exponential form is:

255 = 31×51×171

Now multiplying the highest exponent prime factors to calculate the LCM of 252 and 255.

LCM(252,255) = 22×32×51×71×171
LCM(252,255) = 21420

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

Factors of 255

List of positive integer factors of 255 that divides 255 without a remainder.

1, 3, 5, 15, 17, 51, 85, 255

Least Common Multiple of 252 and 255 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 252 and 255, than apply into the LCM equation.

GCF(252,255) = 3
LCM(252,255) = ( 252 × 255) / 3
LCM(252,255) = 64260 / 3
LCM(252,255) = 21420

Properties of LCM 252 and 255

(i) The LCM of 255 and 252 is associative

LCM of 252 and 255 = LCM of 255 and 252

Related Least Common Multiples of 252

Related Least Common Multiples of 255

Frequently Asked Questions on LCM of 252 and 255

1. What is the LCM of 252 and 255?

Answer: LCM of 252 and 255 is 21420.

2. 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.

3. What are the Factors of 255?

Answer: Factors of 255 are 1, 3, 5, 15, 17, 51, 85, 255. There are 8 integers that are factors of 255. The greatest factor of 255 is 255.

4. How to Find the LCM of 252 and 255?

Answer:

Least Common Multiple of 252 and 255 = 21420

Step 1: Find the prime factorization of 252

252 = 2 x 2 x 3 x 3 x 7

Step 2: Find the prime factorization of 255

255 = 3 x 5 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 = 21420 = 2 x 2 x 3 x 3 x 5 x 7 x 17

Step 4: Therefore, the least common multiple of 252 and 255 is 21420.