Least Common Multiple of 272 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 272 and 278 the smallest integer that is 37808 that is divisible by both numbers.

Least Common Multiple (LCM) of 272 and 278 is 37808.

LCM(272,278) = 37808

LCM of 272 and 278

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

LCM of:
and

Least Common Multiple of 272 and 278

LCM of 272 and 278 is 37808

Least common multiple can be found by multiplying the highest exponent prime factors of 272 and 278. First we will calculate the prime factors of 272 and 278.

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

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 272 and 278.

LCM(272,278) = 24×171×1391
LCM(272,278) = 37808

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

Factors of 278

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

1, 2, 139, 278

Least Common Multiple of 272 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 272 and 278, than apply into the LCM equation.

GCF(272,278) = 2
LCM(272,278) = ( 272 × 278) / 2
LCM(272,278) = 75616 / 2
LCM(272,278) = 37808

Properties of LCM 272 and 278

(i) The LCM of 278 and 272 is associative

LCM of 272 and 278 = LCM of 278 and 272

Related Least Common Multiples of 272

Related Least Common Multiples of 278

Frequently Asked Questions on LCM of 272 and 278

1. What is the LCM of 272 and 278?

Answer: LCM of 272 and 278 is 37808.

2. 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.

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 272 and 278?

Answer:

Least Common Multiple of 272 and 278 = 37808

Step 1: Find the prime factorization of 272

272 = 2 x 2 x 2 x 2 x 17

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 = 37808 = 2 x 2 x 2 x 2 x 17 x 139

Step 4: Therefore, the least common multiple of 272 and 278 is 37808.