Least Common Multiple of 9786 and 9792

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 9786 and 9792 the smallest integer that is 15970752 that is divisible by both numbers.

Least Common Multiple (LCM) of 9786 and 9792 is 15970752.

LCM(9786,9792) = 15970752

LCM of 9786 and 9792

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

LCM of:
and

Least Common Multiple of 9786 and 9792

LCM of 9786 and 9792 is 15970752

Least common multiple can be found by multiplying the highest exponent prime factors of 9786 and 9792. First we will calculate the prime factors of 9786 and 9792.

Prime Factorization of 9786


2 9786
3 4893
7 1631
233 233
1

Prime factors of 9786 are 2, 3, 7,233. Prime factorization of 9786 in exponential form is:

9786 = 21×31×71×2331

Prime Factorization of 9792


2 9792
2 4896
2 2448
2 1224
2 612
2 306
3 153
3 51
17 17
1

Prime factors of 9792 are 2, 3,17. Prime factorization of 9792 in exponential form is:

9792 = 26×32×171

Now multiplying the highest exponent prime factors to calculate the LCM of 9786 and 9792.

LCM(9786,9792) = 26×32×71×171×2331
LCM(9786,9792) = 15970752

Factors of 9786

List of positive integer factors of 9786 that divides 9786 without a remainder.

1, 2, 3, 6, 7, 14, 21, 42, 233, 466, 699, 1398, 1631, 3262, 4893, 9786

Factors of 9792

List of positive integer factors of 9792 that divides 9792 without a remainder.

1, 2, 3, 4, 6, 8, 9, 12, 16, 17, 18, 24, 32, 34, 36, 48, 51, 64, 68, 72, 96, 102, 136, 144, 153, 192, 204, 272, 288, 306, 408, 544, 576, 612, 816, 1088, 1224, 1632, 2448, 3264, 4896, 9792

Least Common Multiple of 9786 and 9792 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 9786 and 9792, than apply into the LCM equation.

GCF(9786,9792) = 6
LCM(9786,9792) = ( 9786 × 9792) / 6
LCM(9786,9792) = 95824512 / 6
LCM(9786,9792) = 15970752

Properties of LCM 9786 and 9792

(i) The LCM of 9792 and 9786 is associative

LCM of 9786 and 9792 = LCM of 9792 and 9786

Related Least Common Multiples of 9786

Related Least Common Multiples of 9792

Frequently Asked Questions on LCM of 9786 and 9792

1. What is the LCM of 9786 and 9792?

Answer: LCM of 9786 and 9792 is 15970752.

2. What are the Factors of 9786?

Answer: Factors of 9786 are 1, 2, 3, 6, 7, 14, 21, 42, 233, 466, 699, 1398, 1631, 3262, 4893, 9786. There are 16 integers that are factors of 9786. The greatest factor of 9786 is 9786.

3. What are the Factors of 9792?

Answer: Factors of 9792 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 17, 18, 24, 32, 34, 36, 48, 51, 64, 68, 72, 96, 102, 136, 144, 153, 192, 204, 272, 288, 306, 408, 544, 576, 612, 816, 1088, 1224, 1632, 2448, 3264, 4896, 9792. There are 42 integers that are factors of 9792. The greatest factor of 9792 is 9792.

4. How to Find the LCM of 9786 and 9792?

Answer:

Least Common Multiple of 9786 and 9792 = 15970752

Step 1: Find the prime factorization of 9786

9786 = 2 x 3 x 7 x 233

Step 2: Find the prime factorization of 9792

9792 = 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 17

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

LCM = 15970752 = 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 7 x 17 x 233

Step 4: Therefore, the least common multiple of 9786 and 9792 is 15970752.