Least Common Multiple of 960 and 963

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 960 and 963 the smallest integer that is 308160 that is divisible by both numbers.

Least Common Multiple (LCM) of 960 and 963 is 308160.

LCM(960,963) = 308160

LCM of 960 and 963

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

LCM of:
and

Least Common Multiple of 960 and 963

LCM of 960 and 963 is 308160

Least common multiple can be found by multiplying the highest exponent prime factors of 960 and 963. First we will calculate the prime factors of 960 and 963.

Prime Factorization of 960


2 960
2 480
2 240
2 120
2 60
2 30
3 15
5 5
1

Prime factors of 960 are 2, 3,5. Prime factorization of 960 in exponential form is:

960 = 26×31×51

Prime Factorization of 963


3 963
3 321
107 107
1

Prime factors of 963 are 3,107. Prime factorization of 963 in exponential form is:

963 = 32×1071

Now multiplying the highest exponent prime factors to calculate the LCM of 960 and 963.

LCM(960,963) = 26×32×51×1071
LCM(960,963) = 308160

Factors of 960

List of positive integer factors of 960 that divides 960 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, 60, 64, 80, 96, 120, 160, 192, 240, 320, 480, 960

Factors of 963

List of positive integer factors of 963 that divides 963 without a remainder.

1, 3, 9, 107, 321, 963

Least Common Multiple of 960 and 963 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 960 and 963, than apply into the LCM equation.

GCF(960,963) = 3
LCM(960,963) = ( 960 × 963) / 3
LCM(960,963) = 924480 / 3
LCM(960,963) = 308160

Properties of LCM 960 and 963

(i) The LCM of 963 and 960 is associative

LCM of 960 and 963 = LCM of 963 and 960

Related Least Common Multiples of 960

Related Least Common Multiples of 963

Frequently Asked Questions on LCM of 960 and 963

1. What is the LCM of 960 and 963?

Answer: LCM of 960 and 963 is 308160.

2. What are the Factors of 960?

Answer: Factors of 960 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, 60, 64, 80, 96, 120, 160, 192, 240, 320, 480, 960. There are 28 integers that are factors of 960. The greatest factor of 960 is 960.

3. What are the Factors of 963?

Answer: Factors of 963 are 1, 3, 9, 107, 321, 963. There are 6 integers that are factors of 963. The greatest factor of 963 is 963.

4. How to Find the LCM of 960 and 963?

Answer:

Least Common Multiple of 960 and 963 = 308160

Step 1: Find the prime factorization of 960

960 = 2 x 2 x 2 x 2 x 2 x 2 x 3 x 5

Step 2: Find the prime factorization of 963

963 = 3 x 3 x 107

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

LCM = 308160 = 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 5 x 107

Step 4: Therefore, the least common multiple of 960 and 963 is 308160.