Least Common Multiple of 354 and 357

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 354 and 357 the smallest integer that is 42126 that is divisible by both numbers.

Least Common Multiple (LCM) of 354 and 357 is 42126.

LCM(354,357) = 42126

LCM of 354 and 357

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

LCM of:
and

Least Common Multiple of 354 and 357

LCM of 354 and 357 is 42126

Least common multiple can be found by multiplying the highest exponent prime factors of 354 and 357. First we will calculate the prime factors of 354 and 357.

Prime Factorization of 354


2 354
3 177
59 59
1

Prime factors of 354 are 2, 3,59. Prime factorization of 354 in exponential form is:

354 = 21×31×591

Prime Factorization of 357


3 357
7 119
17 17
1

Prime factors of 357 are 3, 7,17. Prime factorization of 357 in exponential form is:

357 = 31×71×171

Now multiplying the highest exponent prime factors to calculate the LCM of 354 and 357.

LCM(354,357) = 21×31×71×171×591
LCM(354,357) = 42126

Factors of 354

List of positive integer factors of 354 that divides 354 without a remainder.

1, 2, 3, 6, 59, 118, 177, 354

Factors of 357

List of positive integer factors of 357 that divides 357 without a remainder.

1, 3, 7, 17, 21, 51, 119, 357

Least Common Multiple of 354 and 357 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 354 and 357, than apply into the LCM equation.

GCF(354,357) = 3
LCM(354,357) = ( 354 × 357) / 3
LCM(354,357) = 126378 / 3
LCM(354,357) = 42126

Properties of LCM 354 and 357

(i) The LCM of 357 and 354 is associative

LCM of 354 and 357 = LCM of 357 and 354

Related Least Common Multiples of 354

Related Least Common Multiples of 357

Frequently Asked Questions on LCM of 354 and 357

1. What is the LCM of 354 and 357?

Answer: LCM of 354 and 357 is 42126.

2. What are the Factors of 354?

Answer: Factors of 354 are 1, 2, 3, 6, 59, 118, 177, 354. There are 8 integers that are factors of 354. The greatest factor of 354 is 354.

3. What are the Factors of 357?

Answer: Factors of 357 are 1, 3, 7, 17, 21, 51, 119, 357. There are 8 integers that are factors of 357. The greatest factor of 357 is 357.

4. How to Find the LCM of 354 and 357?

Answer:

Least Common Multiple of 354 and 357 = 42126

Step 1: Find the prime factorization of 354

354 = 2 x 3 x 59

Step 2: Find the prime factorization of 357

357 = 3 x 7 x 17

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

LCM = 42126 = 2 x 3 x 7 x 17 x 59

Step 4: Therefore, the least common multiple of 354 and 357 is 42126.