Least Common Multiple of 9954 and 9960

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 9954 and 9960 the smallest integer that is 16523640 that is divisible by both numbers.

Least Common Multiple (LCM) of 9954 and 9960 is 16523640.

LCM(9954,9960) = 16523640

LCM of 9954 and 9960

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

LCM of:
and

Least Common Multiple of 9954 and 9960

LCM of 9954 and 9960 is 16523640

Least common multiple can be found by multiplying the highest exponent prime factors of 9954 and 9960. First we will calculate the prime factors of 9954 and 9960.

Prime Factorization of 9954


2 9954
3 4977
3 1659
7 553
79 79
1

Prime factors of 9954 are 2, 3, 7,79. Prime factorization of 9954 in exponential form is:

9954 = 21×32×71×791

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

Now multiplying the highest exponent prime factors to calculate the LCM of 9954 and 9960.

LCM(9954,9960) = 23×32×51×71×791×831
LCM(9954,9960) = 16523640

Factors of 9954

List of positive integer factors of 9954 that divides 9954 without a remainder.

1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 63, 79, 126, 158, 237, 474, 553, 711, 1106, 1422, 1659, 3318, 4977, 9954

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

Least Common Multiple of 9954 and 9960 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 9954 and 9960, than apply into the LCM equation.

GCF(9954,9960) = 6
LCM(9954,9960) = ( 9954 × 9960) / 6
LCM(9954,9960) = 99141840 / 6
LCM(9954,9960) = 16523640

Properties of LCM 9954 and 9960

(i) The LCM of 9960 and 9954 is associative

LCM of 9954 and 9960 = LCM of 9960 and 9954

Related Least Common Multiples of 9954

Related Least Common Multiples of 9960

Frequently Asked Questions on LCM of 9954 and 9960

1. What is the LCM of 9954 and 9960?

Answer: LCM of 9954 and 9960 is 16523640.

2. What are the Factors of 9954?

Answer: Factors of 9954 are 1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 63, 79, 126, 158, 237, 474, 553, 711, 1106, 1422, 1659, 3318, 4977, 9954. There are 24 integers that are factors of 9954. The greatest factor of 9954 is 9954.

3. 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.

4. How to Find the LCM of 9954 and 9960?

Answer:

Least Common Multiple of 9954 and 9960 = 16523640

Step 1: Find the prime factorization of 9954

9954 = 2 x 3 x 3 x 7 x 79

Step 2: Find the prime factorization of 9960

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

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

LCM = 16523640 = 2 x 2 x 2 x 3 x 3 x 5 x 7 x 79 x 83

Step 4: Therefore, the least common multiple of 9954 and 9960 is 16523640.