Least Common Multiple of 354 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 354 and 360 the smallest integer that is 21240 that is divisible by both numbers.

Least Common Multiple (LCM) of 354 and 360 is 21240.

LCM(354,360) = 21240

LCM of 354 and 360

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

LCM of:
and

Least Common Multiple of 354 and 360

LCM of 354 and 360 is 21240

Least common multiple can be found by multiplying the highest exponent prime factors of 354 and 360. First we will calculate the prime factors of 354 and 360.

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 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 354 and 360.

LCM(354,360) = 23×32×51×591
LCM(354,360) = 21240

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 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 354 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 354 and 360, than apply into the LCM equation.

GCF(354,360) = 6
LCM(354,360) = ( 354 × 360) / 6
LCM(354,360) = 127440 / 6
LCM(354,360) = 21240

Properties of LCM 354 and 360

(i) The LCM of 360 and 354 is associative

LCM of 354 and 360 = LCM of 360 and 354

Related Least Common Multiples of 354

Related Least Common Multiples of 360

Frequently Asked Questions on LCM of 354 and 360

1. What is the LCM of 354 and 360?

Answer: LCM of 354 and 360 is 21240.

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 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 354 and 360?

Answer:

Least Common Multiple of 354 and 360 = 21240

Step 1: Find the prime factorization of 354

354 = 2 x 3 x 59

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 = 21240 = 2 x 2 x 2 x 3 x 3 x 5 x 59

Step 4: Therefore, the least common multiple of 354 and 360 is 21240.