Least Common Multiple of 357 and 360

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 357 and 360 the smallest integer that is 42840 that is divisible by both numbers.

Least Common Multiple (LCM) of 357 and 360 is 42840.

LCM(357,360) = 42840

LCM of 357 and 360

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

LCM of:
and

Least Common Multiple of 357 and 360

LCM of 357 and 360 is 42840

Least common multiple can be found by multiplying the highest exponent prime factors of 357 and 360. First we will calculate the prime factors of 357 and 360.

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

Prime Factorization of 360


2 360
2 180
2 90
3 45
3 15
5 5
1

Prime factors of 360 are 2, 3,5. Prime factorization of 360 in exponential form is:

360 = 23×32×51

Now multiplying the highest exponent prime factors to calculate the LCM of 357 and 360.

LCM(357,360) = 23×32×51×71×171
LCM(357,360) = 42840

Factors of 357

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

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

Factors of 360

List of positive integer factors of 360 that divides 360 without a remainder.

1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180, 360

Least Common Multiple of 357 and 360 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 357 and 360, than apply into the LCM equation.

GCF(357,360) = 3
LCM(357,360) = ( 357 × 360) / 3
LCM(357,360) = 128520 / 3
LCM(357,360) = 42840

Properties of LCM 357 and 360

(i) The LCM of 360 and 357 is associative

LCM of 357 and 360 = LCM of 360 and 357

Related Least Common Multiples of 357

Related Least Common Multiples of 360

Frequently Asked Questions on LCM of 357 and 360

1. What is the LCM of 357 and 360?

Answer: LCM of 357 and 360 is 42840.

2. 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.

3. What are the Factors of 360?

Answer: Factors of 360 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180, 360. There are 24 integers that are factors of 360. The greatest factor of 360 is 360.

4. How to Find the LCM of 357 and 360?

Answer:

Least Common Multiple of 357 and 360 = 42840

Step 1: Find the prime factorization of 357

357 = 3 x 7 x 17

Step 2: Find the prime factorization of 360

360 = 2 x 2 x 2 x 3 x 3 x 5

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

LCM = 42840 = 2 x 2 x 2 x 3 x 3 x 5 x 7 x 17

Step 4: Therefore, the least common multiple of 357 and 360 is 42840.