Least Common Multiple of 270 and 272

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 270 and 272 the smallest integer that is 36720 that is divisible by both numbers.

Least Common Multiple (LCM) of 270 and 272 is 36720.

LCM(270,272) = 36720

LCM of 270 and 272

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

LCM of:
and

Least Common Multiple of 270 and 272

LCM of 270 and 272 is 36720

Least common multiple can be found by multiplying the highest exponent prime factors of 270 and 272. First we will calculate the prime factors of 270 and 272.

Prime Factorization of 270


2 270
3 135
3 45
3 15
5 5
1

Prime factors of 270 are 2, 3,5. Prime factorization of 270 in exponential form is:

270 = 21×33×51

Prime Factorization of 272


2 272
2 136
2 68
2 34
17 17
1

Prime factors of 272 are 2,17. Prime factorization of 272 in exponential form is:

272 = 24×171

Now multiplying the highest exponent prime factors to calculate the LCM of 270 and 272.

LCM(270,272) = 24×33×51×171
LCM(270,272) = 36720

Factors of 270

List of positive integer factors of 270 that divides 270 without a remainder.

1, 2, 3, 5, 6, 9, 10, 15, 18, 27, 30, 45, 54, 90, 135, 270

Factors of 272

List of positive integer factors of 272 that divides 272 without a remainder.

1, 2, 4, 8, 16, 17, 34, 68, 136, 272

Least Common Multiple of 270 and 272 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 270 and 272, than apply into the LCM equation.

GCF(270,272) = 2
LCM(270,272) = ( 270 × 272) / 2
LCM(270,272) = 73440 / 2
LCM(270,272) = 36720

Properties of LCM 270 and 272

(i) The LCM of 272 and 270 is associative

LCM of 270 and 272 = LCM of 272 and 270

Related Least Common Multiples of 270

Related Least Common Multiples of 272

Frequently Asked Questions on LCM of 270 and 272

1. What is the LCM of 270 and 272?

Answer: LCM of 270 and 272 is 36720.

2. What are the Factors of 270?

Answer: Factors of 270 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 27, 30, 45, 54, 90, 135, 270. There are 16 integers that are factors of 270. The greatest factor of 270 is 270.

3. What are the Factors of 272?

Answer: Factors of 272 are 1, 2, 4, 8, 16, 17, 34, 68, 136, 272. There are 10 integers that are factors of 272. The greatest factor of 272 is 272.

4. How to Find the LCM of 270 and 272?

Answer:

Least Common Multiple of 270 and 272 = 36720

Step 1: Find the prime factorization of 270

270 = 2 x 3 x 3 x 3 x 5

Step 2: Find the prime factorization of 272

272 = 2 x 2 x 2 x 2 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 = 36720 = 2 x 2 x 2 x 2 x 3 x 3 x 3 x 5 x 17

Step 4: Therefore, the least common multiple of 270 and 272 is 36720.