Least Common Multiple of 705 and 706

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 706 the smallest integer that is 497730 that is divisible by both numbers.

Least Common Multiple (LCM) of 705 and 706 is 497730.

LCM(705,706) = 497730

LCM of 705 and 706

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

LCM of:
and

Least Common Multiple of 705 and 706

LCM of 705 and 706 is 497730

Least common multiple can be found by multiplying the highest exponent prime factors of 705 and 706. First we will calculate the prime factors of 705 and 706.

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 706


2 706
353 353
1

Prime factors of 706 are 2,353. Prime factorization of 706 in exponential form is:

706 = 21×3531

Now multiplying the highest exponent prime factors to calculate the LCM of 705 and 706.

LCM(705,706) = 21×31×51×471×3531
LCM(705,706) = 497730

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 706

List of positive integer factors of 706 that divides 706 without a remainder.

1, 2, 353, 706

Least Common Multiple of 705 and 706 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 706, than apply into the LCM equation.

GCF(705,706) = 1
LCM(705,706) = ( 705 × 706) / 1
LCM(705,706) = 497730 / 1
LCM(705,706) = 497730

Properties of LCM 705 and 706

(i) The LCM of 706 and 705 is associative

LCM of 705 and 706 = LCM of 706 and 705

Related Least Common Multiples of 705

Related Least Common Multiples of 706

Frequently Asked Questions on LCM of 705 and 706

1. What is the LCM of 705 and 706?

Answer: LCM of 705 and 706 is 497730.

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 706?

Answer: Factors of 706 are 1, 2, 353, 706. There are 4 integers that are factors of 706. The greatest factor of 706 is 706.

4. How to Find the LCM of 705 and 706?

Answer:

Least Common Multiple of 705 and 706 = 497730

Step 1: Find the prime factorization of 705

705 = 3 x 5 x 47

Step 2: Find the prime factorization of 706

706 = 2 x 353

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

LCM = 497730 = 2 x 3 x 5 x 47 x 353

Step 4: Therefore, the least common multiple of 705 and 706 is 497730.