Least Common Multiple of 9966 and 9972

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 9966 and 9972 the smallest integer that is 16563492 that is divisible by both numbers.

Least Common Multiple (LCM) of 9966 and 9972 is 16563492.

LCM(9966,9972) = 16563492

LCM of 9966 and 9972

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

LCM of:
and

Least Common Multiple of 9966 and 9972

LCM of 9966 and 9972 is 16563492

Least common multiple can be found by multiplying the highest exponent prime factors of 9966 and 9972. First we will calculate the prime factors of 9966 and 9972.

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

Prime Factorization of 9972


2 9972
2 4986
3 2493
3 831
277 277
1

Prime factors of 9972 are 2, 3,277. Prime factorization of 9972 in exponential form is:

9972 = 22×32×2771

Now multiplying the highest exponent prime factors to calculate the LCM of 9966 and 9972.

LCM(9966,9972) = 22×32×111×1511×2771
LCM(9966,9972) = 16563492

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

Factors of 9972

List of positive integer factors of 9972 that divides 9972 without a remainder.

1, 2, 3, 4, 6, 9, 12, 18, 36, 277, 554, 831, 1108, 1662, 2493, 3324, 4986, 9972

Least Common Multiple of 9966 and 9972 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 9966 and 9972, than apply into the LCM equation.

GCF(9966,9972) = 6
LCM(9966,9972) = ( 9966 × 9972) / 6
LCM(9966,9972) = 99380952 / 6
LCM(9966,9972) = 16563492

Properties of LCM 9966 and 9972

(i) The LCM of 9972 and 9966 is associative

LCM of 9966 and 9972 = LCM of 9972 and 9966

Related Least Common Multiples of 9966

Related Least Common Multiples of 9972

Frequently Asked Questions on LCM of 9966 and 9972

1. What is the LCM of 9966 and 9972?

Answer: LCM of 9966 and 9972 is 16563492.

2. 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.

3. What are the Factors of 9972?

Answer: Factors of 9972 are 1, 2, 3, 4, 6, 9, 12, 18, 36, 277, 554, 831, 1108, 1662, 2493, 3324, 4986, 9972. There are 18 integers that are factors of 9972. The greatest factor of 9972 is 9972.

4. How to Find the LCM of 9966 and 9972?

Answer:

Least Common Multiple of 9966 and 9972 = 16563492

Step 1: Find the prime factorization of 9966

9966 = 2 x 3 x 11 x 151

Step 2: Find the prime factorization of 9972

9972 = 2 x 2 x 3 x 3 x 277

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

LCM = 16563492 = 2 x 2 x 3 x 3 x 11 x 151 x 277

Step 4: Therefore, the least common multiple of 9966 and 9972 is 16563492.