Least Common Multiple of 9960 and 9966

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 9960 and 9966 the smallest integer that is 16543560 that is divisible by both numbers.

Least Common Multiple (LCM) of 9960 and 9966 is 16543560.

LCM(9960,9966) = 16543560

LCM of 9960 and 9966

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

LCM of:
and

Least Common Multiple of 9960 and 9966

LCM of 9960 and 9966 is 16543560

Least common multiple can be found by multiplying the highest exponent prime factors of 9960 and 9966. First we will calculate the prime factors of 9960 and 9966.

Prime Factorization of 9960


2 9960
2 4980
2 2490
3 1245
5 415
83 83
1

Prime factors of 9960 are 2, 3, 5,83. Prime factorization of 9960 in exponential form is:

9960 = 23×31×51×831

Prime Factorization of 9966


2 9966
3 4983
11 1661
151 151
1

Prime factors of 9966 are 2, 3, 11,151. Prime factorization of 9966 in exponential form is:

9966 = 21×31×111×1511

Now multiplying the highest exponent prime factors to calculate the LCM of 9960 and 9966.

LCM(9960,9966) = 23×31×51×111×831×1511
LCM(9960,9966) = 16543560

Factors of 9960

List of positive integer factors of 9960 that divides 9960 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 83, 120, 166, 249, 332, 415, 498, 664, 830, 996, 1245, 1660, 1992, 2490, 3320, 4980, 9960

Factors of 9966

List of positive integer factors of 9966 that divides 9966 without a remainder.

1, 2, 3, 6, 11, 22, 33, 66, 151, 302, 453, 906, 1661, 3322, 4983, 9966

Least Common Multiple of 9960 and 9966 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 9960 and 9966, than apply into the LCM equation.

GCF(9960,9966) = 6
LCM(9960,9966) = ( 9960 × 9966) / 6
LCM(9960,9966) = 99261360 / 6
LCM(9960,9966) = 16543560

Properties of LCM 9960 and 9966

(i) The LCM of 9966 and 9960 is associative

LCM of 9960 and 9966 = LCM of 9966 and 9960

Related Least Common Multiples of 9960

Related Least Common Multiples of 9966

Frequently Asked Questions on LCM of 9960 and 9966

1. What is the LCM of 9960 and 9966?

Answer: LCM of 9960 and 9966 is 16543560.

2. What are the Factors of 9960?

Answer: Factors of 9960 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 83, 120, 166, 249, 332, 415, 498, 664, 830, 996, 1245, 1660, 1992, 2490, 3320, 4980, 9960. There are 32 integers that are factors of 9960. The greatest factor of 9960 is 9960.

3. What are the Factors of 9966?

Answer: Factors of 9966 are 1, 2, 3, 6, 11, 22, 33, 66, 151, 302, 453, 906, 1661, 3322, 4983, 9966. There are 16 integers that are factors of 9966. The greatest factor of 9966 is 9966.

4. How to Find the LCM of 9960 and 9966?

Answer:

Least Common Multiple of 9960 and 9966 = 16543560

Step 1: Find the prime factorization of 9960

9960 = 2 x 2 x 2 x 3 x 5 x 83

Step 2: Find the prime factorization of 9966

9966 = 2 x 3 x 11 x 151

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

LCM = 16543560 = 2 x 2 x 2 x 3 x 5 x 11 x 83 x 151

Step 4: Therefore, the least common multiple of 9960 and 9966 is 16543560.