Least Common Multiple of 705 and 712

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 712 the smallest integer that is 501960 that is divisible by both numbers.

Least Common Multiple (LCM) of 705 and 712 is 501960.

LCM(705,712) = 501960

LCM of 705 and 712

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

LCM of:
and

Least Common Multiple of 705 and 712

LCM of 705 and 712 is 501960

Least common multiple can be found by multiplying the highest exponent prime factors of 705 and 712. First we will calculate the prime factors of 705 and 712.

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 712


2 712
2 356
2 178
89 89
1

Prime factors of 712 are 2,89. Prime factorization of 712 in exponential form is:

712 = 23×891

Now multiplying the highest exponent prime factors to calculate the LCM of 705 and 712.

LCM(705,712) = 23×31×51×471×891
LCM(705,712) = 501960

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 712

List of positive integer factors of 712 that divides 712 without a remainder.

1, 2, 4, 8, 89, 178, 356, 712

Least Common Multiple of 705 and 712 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 712, than apply into the LCM equation.

GCF(705,712) = 1
LCM(705,712) = ( 705 × 712) / 1
LCM(705,712) = 501960 / 1
LCM(705,712) = 501960

Properties of LCM 705 and 712

(i) The LCM of 712 and 705 is associative

LCM of 705 and 712 = LCM of 712 and 705

Related Least Common Multiples of 705

Related Least Common Multiples of 712

Frequently Asked Questions on LCM of 705 and 712

1. What is the LCM of 705 and 712?

Answer: LCM of 705 and 712 is 501960.

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 712?

Answer: Factors of 712 are 1, 2, 4, 8, 89, 178, 356, 712. There are 8 integers that are factors of 712. The greatest factor of 712 is 712.

4. How to Find the LCM of 705 and 712?

Answer:

Least Common Multiple of 705 and 712 = 501960

Step 1: Find the prime factorization of 705

705 = 3 x 5 x 47

Step 2: Find the prime factorization of 712

712 = 2 x 2 x 2 x 89

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

LCM = 501960 = 2 x 2 x 2 x 3 x 5 x 47 x 89

Step 4: Therefore, the least common multiple of 705 and 712 is 501960.