Least Common Multiple of 480 and 486

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 480 and 486 the smallest integer that is 38880 that is divisible by both numbers.

Least Common Multiple (LCM) of 480 and 486 is 38880.

LCM(480,486) = 38880

LCM of 480 and 486

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

LCM of:
and

Least Common Multiple of 480 and 486

LCM of 480 and 486 is 38880

Least common multiple can be found by multiplying the highest exponent prime factors of 480 and 486. First we will calculate the prime factors of 480 and 486.

Prime Factorization of 480


2 480
2 240
2 120
2 60
2 30
3 15
5 5
1

Prime factors of 480 are 2, 3,5. Prime factorization of 480 in exponential form is:

480 = 25×31×51

Prime Factorization of 486


2 486
3 243
3 81
3 27
3 9
3 3
1

Prime factors of 486 are 2,3. Prime factorization of 486 in exponential form is:

486 = 21×35

Now multiplying the highest exponent prime factors to calculate the LCM of 480 and 486.

LCM(480,486) = 25×35×51
LCM(480,486) = 38880

Factors of 480

List of positive integer factors of 480 that divides 480 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, 60, 80, 96, 120, 160, 240, 480

Factors of 486

List of positive integer factors of 486 that divides 486 without a remainder.

1, 2, 3, 6, 9, 18, 27, 54, 81, 162, 243, 486

Least Common Multiple of 480 and 486 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 480 and 486, than apply into the LCM equation.

GCF(480,486) = 6
LCM(480,486) = ( 480 × 486) / 6
LCM(480,486) = 233280 / 6
LCM(480,486) = 38880

Properties of LCM 480 and 486

(i) The LCM of 486 and 480 is associative

LCM of 480 and 486 = LCM of 486 and 480

Related Least Common Multiples of 480

Related Least Common Multiples of 486

Frequently Asked Questions on LCM of 480 and 486

1. What is the LCM of 480 and 486?

Answer: LCM of 480 and 486 is 38880.

2. What are the Factors of 480?

Answer: Factors of 480 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, 60, 80, 96, 120, 160, 240, 480. There are 24 integers that are factors of 480. The greatest factor of 480 is 480.

3. What are the Factors of 486?

Answer: Factors of 486 are 1, 2, 3, 6, 9, 18, 27, 54, 81, 162, 243, 486. There are 12 integers that are factors of 486. The greatest factor of 486 is 486.

4. How to Find the LCM of 480 and 486?

Answer:

Least Common Multiple of 480 and 486 = 38880

Step 1: Find the prime factorization of 480

480 = 2 x 2 x 2 x 2 x 2 x 3 x 5

Step 2: Find the prime factorization of 486

486 = 2 x 3 x 3 x 3 x 3 x 3

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

LCM = 38880 = 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3 x 3 x 3 x 5

Step 4: Therefore, the least common multiple of 480 and 486 is 38880.