Least Common Multiple of 705 and 708

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 705 and 708 the smallest integer that is 166380 that is divisible by both numbers.

Least Common Multiple (LCM) of 705 and 708 is 166380.

LCM(705,708) = 166380

LCM of 705 and 708

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

LCM of:
and

Least Common Multiple of 705 and 708

LCM of 705 and 708 is 166380

Least common multiple can be found by multiplying the highest exponent prime factors of 705 and 708. First we will calculate the prime factors of 705 and 708.

Prime Factorization of 705


3 705
5 235
47 47
1

Prime factors of 705 are 3, 5,47. Prime factorization of 705 in exponential form is:

705 = 31×51×471

Prime Factorization of 708


2 708
2 354
3 177
59 59
1

Prime factors of 708 are 2, 3,59. Prime factorization of 708 in exponential form is:

708 = 22×31×591

Now multiplying the highest exponent prime factors to calculate the LCM of 705 and 708.

LCM(705,708) = 22×31×51×471×591
LCM(705,708) = 166380

Factors of 705

List of positive integer factors of 705 that divides 705 without a remainder.

1, 3, 5, 15, 47, 141, 235, 705

Factors of 708

List of positive integer factors of 708 that divides 708 without a remainder.

1, 2, 3, 4, 6, 12, 59, 118, 177, 236, 354, 708

Least Common Multiple of 705 and 708 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 705 and 708, than apply into the LCM equation.

GCF(705,708) = 3
LCM(705,708) = ( 705 × 708) / 3
LCM(705,708) = 499140 / 3
LCM(705,708) = 166380

Properties of LCM 705 and 708

(i) The LCM of 708 and 705 is associative

LCM of 705 and 708 = LCM of 708 and 705

Related Least Common Multiples of 705

Related Least Common Multiples of 708

Frequently Asked Questions on LCM of 705 and 708

1. What is the LCM of 705 and 708?

Answer: LCM of 705 and 708 is 166380.

2. What are the Factors of 705?

Answer: Factors of 705 are 1, 3, 5, 15, 47, 141, 235, 705. There are 8 integers that are factors of 705. The greatest factor of 705 is 705.

3. What are the Factors of 708?

Answer: Factors of 708 are 1, 2, 3, 4, 6, 12, 59, 118, 177, 236, 354, 708. There are 12 integers that are factors of 708. The greatest factor of 708 is 708.

4. How to Find the LCM of 705 and 708?

Answer:

Least Common Multiple of 705 and 708 = 166380

Step 1: Find the prime factorization of 705

705 = 3 x 5 x 47

Step 2: Find the prime factorization of 708

708 = 2 x 2 x 3 x 59

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

LCM = 166380 = 2 x 2 x 3 x 5 x 47 x 59

Step 4: Therefore, the least common multiple of 705 and 708 is 166380.