Least Common Multiple of 274 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 274 and 280 the smallest integer that is 38360 that is divisible by both numbers.

Least Common Multiple (LCM) of 274 and 280 is 38360.

LCM(274,280) = 38360

LCM of 274 and 280

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

LCM of:
and

Least Common Multiple of 274 and 280

LCM of 274 and 280 is 38360

Least common multiple can be found by multiplying the highest exponent prime factors of 274 and 280. First we will calculate the prime factors of 274 and 280.

Prime Factorization of 274


2 274
137 137
1

Prime factors of 274 are 2,137. Prime factorization of 274 in exponential form is:

274 = 21×1371

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 274 and 280.

LCM(274,280) = 23×51×71×1371
LCM(274,280) = 38360

Factors of 274

List of positive integer factors of 274 that divides 274 without a remainder.

1, 2, 137, 274

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 274 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 274 and 280, than apply into the LCM equation.

GCF(274,280) = 2
LCM(274,280) = ( 274 × 280) / 2
LCM(274,280) = 76720 / 2
LCM(274,280) = 38360

Properties of LCM 274 and 280

(i) The LCM of 280 and 274 is associative

LCM of 274 and 280 = LCM of 280 and 274

Related Least Common Multiples of 274

Related Least Common Multiples of 280

Frequently Asked Questions on LCM of 274 and 280

1. What is the LCM of 274 and 280?

Answer: LCM of 274 and 280 is 38360.

2. What are the Factors of 274?

Answer: Factors of 274 are 1, 2, 137, 274. There are 4 integers that are factors of 274. The greatest factor of 274 is 274.

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 274 and 280?

Answer:

Least Common Multiple of 274 and 280 = 38360

Step 1: Find the prime factorization of 274

274 = 2 x 137

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 = 38360 = 2 x 2 x 2 x 5 x 7 x 137

Step 4: Therefore, the least common multiple of 274 and 280 is 38360.