Least Common Multiple of 960 and 966

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 966 the smallest integer that is 154560 that is divisible by both numbers.

Least Common Multiple (LCM) of 960 and 966 is 154560.

LCM(960,966) = 154560

LCM of 960 and 966

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

LCM of:
and

Least Common Multiple of 960 and 966

LCM of 960 and 966 is 154560

Least common multiple can be found by multiplying the highest exponent prime factors of 960 and 966. First we will calculate the prime factors of 960 and 966.

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 966


2 966
3 483
7 161
23 23
1

Prime factors of 966 are 2, 3, 7,23. Prime factorization of 966 in exponential form is:

966 = 21×31×71×231

Now multiplying the highest exponent prime factors to calculate the LCM of 960 and 966.

LCM(960,966) = 26×31×51×71×231
LCM(960,966) = 154560

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 966

List of positive integer factors of 966 that divides 966 without a remainder.

1, 2, 3, 6, 7, 14, 21, 23, 42, 46, 69, 138, 161, 322, 483, 966

Least Common Multiple of 960 and 966 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 966, than apply into the LCM equation.

GCF(960,966) = 6
LCM(960,966) = ( 960 × 966) / 6
LCM(960,966) = 927360 / 6
LCM(960,966) = 154560

Properties of LCM 960 and 966

(i) The LCM of 966 and 960 is associative

LCM of 960 and 966 = LCM of 966 and 960

Related Least Common Multiples of 960

Related Least Common Multiples of 966

Frequently Asked Questions on LCM of 960 and 966

1. What is the LCM of 960 and 966?

Answer: LCM of 960 and 966 is 154560.

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 966?

Answer: Factors of 966 are 1, 2, 3, 6, 7, 14, 21, 23, 42, 46, 69, 138, 161, 322, 483, 966. There are 16 integers that are factors of 966. The greatest factor of 966 is 966.

4. How to Find the LCM of 960 and 966?

Answer:

Least Common Multiple of 960 and 966 = 154560

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 966

966 = 2 x 3 x 7 x 23

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

LCM = 154560 = 2 x 2 x 2 x 2 x 2 x 2 x 3 x 5 x 7 x 23

Step 4: Therefore, the least common multiple of 960 and 966 is 154560.