Least Common Multiple of 9717 and 9720

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 9717 and 9720 the smallest integer that is 31483080 that is divisible by both numbers.

Least Common Multiple (LCM) of 9717 and 9720 is 31483080.

LCM(9717,9720) = 31483080

LCM of 9717 and 9720

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

LCM of:
and

Least Common Multiple of 9717 and 9720

LCM of 9717 and 9720 is 31483080

Least common multiple can be found by multiplying the highest exponent prime factors of 9717 and 9720. First we will calculate the prime factors of 9717 and 9720.

Prime Factorization of 9717


3 9717
41 3239
79 79
1

Prime factors of 9717 are 3, 41,79. Prime factorization of 9717 in exponential form is:

9717 = 31×411×791

Prime Factorization of 9720


2 9720
2 4860
2 2430
3 1215
3 405
3 135
3 45
3 15
5 5
1

Prime factors of 9720 are 2, 3,5. Prime factorization of 9720 in exponential form is:

9720 = 23×35×51

Now multiplying the highest exponent prime factors to calculate the LCM of 9717 and 9720.

LCM(9717,9720) = 23×35×51×411×791
LCM(9717,9720) = 31483080

Factors of 9717

List of positive integer factors of 9717 that divides 9717 without a remainder.

1, 3, 41, 79, 123, 237, 3239, 9717

Factors of 9720

List of positive integer factors of 9720 that divides 9720 without a remainder.

1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 27, 30, 36, 40, 45, 54, 60, 72, 81, 90, 108, 120, 135, 162, 180, 216, 243, 270, 324, 360, 405, 486, 540, 648, 810, 972, 1080, 1215, 1620, 1944, 2430, 3240, 4860, 9720

Least Common Multiple of 9717 and 9720 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 9717 and 9720, than apply into the LCM equation.

GCF(9717,9720) = 3
LCM(9717,9720) = ( 9717 × 9720) / 3
LCM(9717,9720) = 94449240 / 3
LCM(9717,9720) = 31483080

Properties of LCM 9717 and 9720

(i) The LCM of 9720 and 9717 is associative

LCM of 9717 and 9720 = LCM of 9720 and 9717

Related Least Common Multiples of 9717

Related Least Common Multiples of 9720

Frequently Asked Questions on LCM of 9717 and 9720

1. What is the LCM of 9717 and 9720?

Answer: LCM of 9717 and 9720 is 31483080.

2. What are the Factors of 9717?

Answer: Factors of 9717 are 1, 3, 41, 79, 123, 237, 3239, 9717. There are 8 integers that are factors of 9717. The greatest factor of 9717 is 9717.

3. What are the Factors of 9720?

Answer: Factors of 9720 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 27, 30, 36, 40, 45, 54, 60, 72, 81, 90, 108, 120, 135, 162, 180, 216, 243, 270, 324, 360, 405, 486, 540, 648, 810, 972, 1080, 1215, 1620, 1944, 2430, 3240, 4860, 9720. There are 48 integers that are factors of 9720. The greatest factor of 9720 is 9720.

4. How to Find the LCM of 9717 and 9720?

Answer:

Least Common Multiple of 9717 and 9720 = 31483080

Step 1: Find the prime factorization of 9717

9717 = 3 x 41 x 79

Step 2: Find the prime factorization of 9720

9720 = 2 x 2 x 2 x 3 x 3 x 3 x 3 x 3 x 5

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

LCM = 31483080 = 2 x 2 x 2 x 3 x 3 x 3 x 3 x 3 x 5 x 41 x 79

Step 4: Therefore, the least common multiple of 9717 and 9720 is 31483080.