Least Common Multiple of 278 and 280

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 278 and 280 the smallest integer that is 38920 that is divisible by both numbers.

Least Common Multiple (LCM) of 278 and 280 is 38920.

LCM(278,280) = 38920

LCM of 278 and 280

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

LCM of:
and

Least Common Multiple of 278 and 280

LCM of 278 and 280 is 38920

Least common multiple can be found by multiplying the highest exponent prime factors of 278 and 280. First we will calculate the prime factors of 278 and 280.

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

Prime Factorization of 280


2 280
2 140
2 70
5 35
7 7
1

Prime factors of 280 are 2, 5,7. Prime factorization of 280 in exponential form is:

280 = 23×51×71

Now multiplying the highest exponent prime factors to calculate the LCM of 278 and 280.

LCM(278,280) = 23×51×71×1391
LCM(278,280) = 38920

Factors of 278

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

1, 2, 139, 278

Factors of 280

List of positive integer factors of 280 that divides 280 without a remainder.

1, 2, 4, 5, 7, 8, 10, 14, 20, 28, 35, 40, 56, 70, 140, 280

Least Common Multiple of 278 and 280 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 278 and 280, than apply into the LCM equation.

GCF(278,280) = 2
LCM(278,280) = ( 278 × 280) / 2
LCM(278,280) = 77840 / 2
LCM(278,280) = 38920

Properties of LCM 278 and 280

(i) The LCM of 280 and 278 is associative

LCM of 278 and 280 = LCM of 280 and 278

Related Least Common Multiples of 278

Related Least Common Multiples of 280

Frequently Asked Questions on LCM of 278 and 280

1. What is the LCM of 278 and 280?

Answer: LCM of 278 and 280 is 38920.

2. 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.

3. What are the Factors of 280?

Answer: Factors of 280 are 1, 2, 4, 5, 7, 8, 10, 14, 20, 28, 35, 40, 56, 70, 140, 280. There are 16 integers that are factors of 280. The greatest factor of 280 is 280.

4. How to Find the LCM of 278 and 280?

Answer:

Least Common Multiple of 278 and 280 = 38920

Step 1: Find the prime factorization of 278

278 = 2 x 139

Step 2: Find the prime factorization of 280

280 = 2 x 2 x 2 x 5 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 = 38920 = 2 x 2 x 2 x 5 x 7 x 139

Step 4: Therefore, the least common multiple of 278 and 280 is 38920.