Least Common Multiple of 9785 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 9785 and 9792 the smallest integer that is 95814720 that is divisible by both numbers.

Least Common Multiple (LCM) of 9785 and 9792 is 95814720.

LCM(9785,9792) = 95814720

LCM of 9785 and 9792

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

LCM of:
and

Least Common Multiple of 9785 and 9792

LCM of 9785 and 9792 is 95814720

Least common multiple can be found by multiplying the highest exponent prime factors of 9785 and 9792. First we will calculate the prime factors of 9785 and 9792.

Prime Factorization of 9785


5 9785
19 1957
103 103
1

Prime factors of 9785 are 5, 19,103. Prime factorization of 9785 in exponential form is:

9785 = 51×191×1031

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 9785 and 9792.

LCM(9785,9792) = 26×32×51×171×191×1031
LCM(9785,9792) = 95814720

Factors of 9785

List of positive integer factors of 9785 that divides 9785 without a remainder.

1, 5, 19, 95, 103, 515, 1957, 9785

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 9785 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 9785 and 9792, than apply into the LCM equation.

GCF(9785,9792) = 1
LCM(9785,9792) = ( 9785 × 9792) / 1
LCM(9785,9792) = 95814720 / 1
LCM(9785,9792) = 95814720

Properties of LCM 9785 and 9792

(i) The LCM of 9792 and 9785 is associative

LCM of 9785 and 9792 = LCM of 9792 and 9785

Related Least Common Multiples of 9785

Related Least Common Multiples of 9792

Frequently Asked Questions on LCM of 9785 and 9792

1. What is the LCM of 9785 and 9792?

Answer: LCM of 9785 and 9792 is 95814720.

2. What are the Factors of 9785?

Answer: Factors of 9785 are 1, 5, 19, 95, 103, 515, 1957, 9785. There are 8 integers that are factors of 9785. The greatest factor of 9785 is 9785.

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 9785 and 9792?

Answer:

Least Common Multiple of 9785 and 9792 = 95814720

Step 1: Find the prime factorization of 9785

9785 = 5 x 19 x 103

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 = 95814720 = 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 5 x 17 x 19 x 103

Step 4: Therefore, the least common multiple of 9785 and 9792 is 95814720.