Least Common Multiple of 9960 and 9965

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 9965 the smallest integer that is 19850280 that is divisible by both numbers.

Least Common Multiple (LCM) of 9960 and 9965 is 19850280.

LCM(9960,9965) = 19850280

LCM of 9960 and 9965

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

LCM of:
and

Least Common Multiple of 9960 and 9965

LCM of 9960 and 9965 is 19850280

Least common multiple can be found by multiplying the highest exponent prime factors of 9960 and 9965. First we will calculate the prime factors of 9960 and 9965.

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 9965


5 9965
1993 1993
1

Prime factors of 9965 are 5,1993. Prime factorization of 9965 in exponential form is:

9965 = 51×19931

Now multiplying the highest exponent prime factors to calculate the LCM of 9960 and 9965.

LCM(9960,9965) = 23×31×51×831×19931
LCM(9960,9965) = 19850280

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 9965

List of positive integer factors of 9965 that divides 9965 without a remainder.

1, 5, 1993, 9965

Least Common Multiple of 9960 and 9965 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 9965, than apply into the LCM equation.

GCF(9960,9965) = 5
LCM(9960,9965) = ( 9960 × 9965) / 5
LCM(9960,9965) = 99251400 / 5
LCM(9960,9965) = 19850280

Properties of LCM 9960 and 9965

(i) The LCM of 9965 and 9960 is associative

LCM of 9960 and 9965 = LCM of 9965 and 9960

Related Least Common Multiples of 9960

Related Least Common Multiples of 9965

Frequently Asked Questions on LCM of 9960 and 9965

1. What is the LCM of 9960 and 9965?

Answer: LCM of 9960 and 9965 is 19850280.

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 9965?

Answer: Factors of 9965 are 1, 5, 1993, 9965. There are 4 integers that are factors of 9965. The greatest factor of 9965 is 9965.

4. How to Find the LCM of 9960 and 9965?

Answer:

Least Common Multiple of 9960 and 9965 = 19850280

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 9965

9965 = 5 x 1993

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

LCM = 19850280 = 2 x 2 x 2 x 3 x 5 x 83 x 1993

Step 4: Therefore, the least common multiple of 9960 and 9965 is 19850280.