Least Common Multiple of 700 and 704

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 700 and 704 the smallest integer that is 123200 that is divisible by both numbers.

Least Common Multiple (LCM) of 700 and 704 is 123200.

LCM(700,704) = 123200

LCM of 700 and 704

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

LCM of:
and

Least Common Multiple of 700 and 704

LCM of 700 and 704 is 123200

Least common multiple can be found by multiplying the highest exponent prime factors of 700 and 704. First we will calculate the prime factors of 700 and 704.

Prime Factorization of 700


2 700
2 350
5 175
5 35
7 7
1

Prime factors of 700 are 2, 5,7. Prime factorization of 700 in exponential form is:

700 = 22×52×71

Prime Factorization of 704


2 704
2 352
2 176
2 88
2 44
2 22
11 11
1

Prime factors of 704 are 2,11. Prime factorization of 704 in exponential form is:

704 = 26×111

Now multiplying the highest exponent prime factors to calculate the LCM of 700 and 704.

LCM(700,704) = 26×52×71×111
LCM(700,704) = 123200

Factors of 700

List of positive integer factors of 700 that divides 700 without a remainder.

1, 2, 4, 5, 7, 10, 14, 20, 25, 28, 35, 50, 70, 100, 140, 175, 350, 700

Factors of 704

List of positive integer factors of 704 that divides 704 without a remainder.

1, 2, 4, 8, 11, 16, 22, 32, 44, 64, 88, 176, 352, 704

Least Common Multiple of 700 and 704 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 700 and 704, than apply into the LCM equation.

GCF(700,704) = 4
LCM(700,704) = ( 700 × 704) / 4
LCM(700,704) = 492800 / 4
LCM(700,704) = 123200

Properties of LCM 700 and 704

(i) The LCM of 704 and 700 is associative

LCM of 700 and 704 = LCM of 704 and 700

Related Least Common Multiples of 700

Related Least Common Multiples of 704

Frequently Asked Questions on LCM of 700 and 704

1. What is the LCM of 700 and 704?

Answer: LCM of 700 and 704 is 123200.

2. What are the Factors of 700?

Answer: Factors of 700 are 1, 2, 4, 5, 7, 10, 14, 20, 25, 28, 35, 50, 70, 100, 140, 175, 350, 700. There are 18 integers that are factors of 700. The greatest factor of 700 is 700.

3. What are the Factors of 704?

Answer: Factors of 704 are 1, 2, 4, 8, 11, 16, 22, 32, 44, 64, 88, 176, 352, 704. There are 14 integers that are factors of 704. The greatest factor of 704 is 704.

4. How to Find the LCM of 700 and 704?

Answer:

Least Common Multiple of 700 and 704 = 123200

Step 1: Find the prime factorization of 700

700 = 2 x 2 x 5 x 5 x 7

Step 2: Find the prime factorization of 704

704 = 2 x 2 x 2 x 2 x 2 x 2 x 11

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

LCM = 123200 = 2 x 2 x 2 x 2 x 2 x 2 x 5 x 5 x 7 x 11

Step 4: Therefore, the least common multiple of 700 and 704 is 123200.