Least Common Multiple of 268 and 274

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 268 and 274 the smallest integer that is 36716 that is divisible by both numbers.

Least Common Multiple (LCM) of 268 and 274 is 36716.

LCM(268,274) = 36716

LCM of 268 and 274

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

LCM of:
and

Least Common Multiple of 268 and 274

LCM of 268 and 274 is 36716

Least common multiple can be found by multiplying the highest exponent prime factors of 268 and 274. First we will calculate the prime factors of 268 and 274.

Prime Factorization of 268


2 268
2 134
67 67
1

Prime factors of 268 are 2,67. Prime factorization of 268 in exponential form is:

268 = 22×671

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

Now multiplying the highest exponent prime factors to calculate the LCM of 268 and 274.

LCM(268,274) = 22×671×1371
LCM(268,274) = 36716

Factors of 268

List of positive integer factors of 268 that divides 268 without a remainder.

1, 2, 4, 67, 134, 268

Factors of 274

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

1, 2, 137, 274

Least Common Multiple of 268 and 274 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 268 and 274, than apply into the LCM equation.

GCF(268,274) = 2
LCM(268,274) = ( 268 × 274) / 2
LCM(268,274) = 73432 / 2
LCM(268,274) = 36716

Properties of LCM 268 and 274

(i) The LCM of 274 and 268 is associative

LCM of 268 and 274 = LCM of 274 and 268

Related Least Common Multiples of 268

Related Least Common Multiples of 274

Frequently Asked Questions on LCM of 268 and 274

1. What is the LCM of 268 and 274?

Answer: LCM of 268 and 274 is 36716.

2. What are the Factors of 268?

Answer: Factors of 268 are 1, 2, 4, 67, 134, 268. There are 6 integers that are factors of 268. The greatest factor of 268 is 268.

3. 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.

4. How to Find the LCM of 268 and 274?

Answer:

Least Common Multiple of 268 and 274 = 36716

Step 1: Find the prime factorization of 268

268 = 2 x 2 x 67

Step 2: Find the prime factorization of 274

274 = 2 x 137

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

LCM = 36716 = 2 x 2 x 67 x 137

Step 4: Therefore, the least common multiple of 268 and 274 is 36716.