Least Common Multiple of 270 and 278

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 278 the smallest integer that is 37530 that is divisible by both numbers.

Least Common Multiple (LCM) of 270 and 278 is 37530.

LCM(270,278) = 37530

LCM of 270 and 278

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

LCM of:
and

Least Common Multiple of 270 and 278

LCM of 270 and 278 is 37530

Least common multiple can be found by multiplying the highest exponent prime factors of 270 and 278. First we will calculate the prime factors of 270 and 278.

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 278


2 278
139 139
1

Prime factors of 278 are 2,139. Prime factorization of 278 in exponential form is:

278 = 21×1391

Now multiplying the highest exponent prime factors to calculate the LCM of 270 and 278.

LCM(270,278) = 21×33×51×1391
LCM(270,278) = 37530

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 278

List of positive integer factors of 278 that divides 278 without a remainder.

1, 2, 139, 278

Least Common Multiple of 270 and 278 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 278, than apply into the LCM equation.

GCF(270,278) = 2
LCM(270,278) = ( 270 × 278) / 2
LCM(270,278) = 75060 / 2
LCM(270,278) = 37530

Properties of LCM 270 and 278

(i) The LCM of 278 and 270 is associative

LCM of 270 and 278 = LCM of 278 and 270

Related Least Common Multiples of 270

Related Least Common Multiples of 278

Frequently Asked Questions on LCM of 270 and 278

1. What is the LCM of 270 and 278?

Answer: LCM of 270 and 278 is 37530.

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 278?

Answer: Factors of 278 are 1, 2, 139, 278. There are 4 integers that are factors of 278. The greatest factor of 278 is 278.

4. How to Find the LCM of 270 and 278?

Answer:

Least Common Multiple of 270 and 278 = 37530

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 278

278 = 2 x 139

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

LCM = 37530 = 2 x 3 x 3 x 3 x 5 x 139

Step 4: Therefore, the least common multiple of 270 and 278 is 37530.