Least Common Multiple of 705 and 713

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 713 the smallest integer that is 502665 that is divisible by both numbers.

Least Common Multiple (LCM) of 705 and 713 is 502665.

LCM(705,713) = 502665

LCM of 705 and 713

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

LCM of:
and

Least Common Multiple of 705 and 713

LCM of 705 and 713 is 502665

Least common multiple can be found by multiplying the highest exponent prime factors of 705 and 713. First we will calculate the prime factors of 705 and 713.

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 713


23 713
31 31
1

Prime factors of 713 are 23,31. Prime factorization of 713 in exponential form is:

713 = 231×311

Now multiplying the highest exponent prime factors to calculate the LCM of 705 and 713.

LCM(705,713) = 31×51×231×311×471
LCM(705,713) = 502665

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 713

List of positive integer factors of 713 that divides 713 without a remainder.

1, 23, 31, 713

Least Common Multiple of 705 and 713 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 713, than apply into the LCM equation.

GCF(705,713) = 1
LCM(705,713) = ( 705 × 713) / 1
LCM(705,713) = 502665 / 1
LCM(705,713) = 502665

Properties of LCM 705 and 713

(i) The LCM of 713 and 705 is associative

LCM of 705 and 713 = LCM of 713 and 705

Related Least Common Multiples of 705

Related Least Common Multiples of 713

Frequently Asked Questions on LCM of 705 and 713

1. What is the LCM of 705 and 713?

Answer: LCM of 705 and 713 is 502665.

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 713?

Answer: Factors of 713 are 1, 23, 31, 713. There are 4 integers that are factors of 713. The greatest factor of 713 is 713.

4. How to Find the LCM of 705 and 713?

Answer:

Least Common Multiple of 705 and 713 = 502665

Step 1: Find the prime factorization of 705

705 = 3 x 5 x 47

Step 2: Find the prime factorization of 713

713 = 23 x 31

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

LCM = 502665 = 3 x 5 x 23 x 31 x 47

Step 4: Therefore, the least common multiple of 705 and 713 is 502665.