Least Common Multiple of 780 and 784

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 780 and 784 the smallest integer that is 152880 that is divisible by both numbers.

Least Common Multiple (LCM) of 780 and 784 is 152880.

LCM(780,784) = 152880

LCM of 780 and 784

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

LCM of:
and

Least Common Multiple of 780 and 784

LCM of 780 and 784 is 152880

Least common multiple can be found by multiplying the highest exponent prime factors of 780 and 784. First we will calculate the prime factors of 780 and 784.

Prime Factorization of 780


2 780
2 390
3 195
5 65
13 13
1

Prime factors of 780 are 2, 3, 5,13. Prime factorization of 780 in exponential form is:

780 = 22×31×51×131

Prime Factorization of 784


2 784
2 392
2 196
2 98
7 49
7 7
1

Prime factors of 784 are 2,7. Prime factorization of 784 in exponential form is:

784 = 24×72

Now multiplying the highest exponent prime factors to calculate the LCM of 780 and 784.

LCM(780,784) = 24×31×51×72×131
LCM(780,784) = 152880

Factors of 780

List of positive integer factors of 780 that divides 780 without a remainder.

1, 2, 3, 4, 5, 6, 10, 12, 13, 15, 20, 26, 30, 39, 52, 60, 65, 78, 130, 156, 195, 260, 390, 780

Factors of 784

List of positive integer factors of 784 that divides 784 without a remainder.

1, 2, 4, 7, 8, 14, 16, 28, 49, 56, 98, 112, 196, 392, 784

Least Common Multiple of 780 and 784 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 780 and 784, than apply into the LCM equation.

GCF(780,784) = 4
LCM(780,784) = ( 780 × 784) / 4
LCM(780,784) = 611520 / 4
LCM(780,784) = 152880

Properties of LCM 780 and 784

(i) The LCM of 784 and 780 is associative

LCM of 780 and 784 = LCM of 784 and 780

Related Least Common Multiples of 780

Related Least Common Multiples of 784

Frequently Asked Questions on LCM of 780 and 784

1. What is the LCM of 780 and 784?

Answer: LCM of 780 and 784 is 152880.

2. What are the Factors of 780?

Answer: Factors of 780 are 1, 2, 3, 4, 5, 6, 10, 12, 13, 15, 20, 26, 30, 39, 52, 60, 65, 78, 130, 156, 195, 260, 390, 780. There are 24 integers that are factors of 780. The greatest factor of 780 is 780.

3. What are the Factors of 784?

Answer: Factors of 784 are 1, 2, 4, 7, 8, 14, 16, 28, 49, 56, 98, 112, 196, 392, 784. There are 15 integers that are factors of 784. The greatest factor of 784 is 784.

4. How to Find the LCM of 780 and 784?

Answer:

Least Common Multiple of 780 and 784 = 152880

Step 1: Find the prime factorization of 780

780 = 2 x 2 x 3 x 5 x 13

Step 2: Find the prime factorization of 784

784 = 2 x 2 x 2 x 2 x 7 x 7

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

LCM = 152880 = 2 x 2 x 2 x 2 x 3 x 5 x 7 x 7 x 13

Step 4: Therefore, the least common multiple of 780 and 784 is 152880.