Least Common Multiple of 31306 and 31312

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 31306 and 31312 the smallest integer that is 490126736 that is divisible by both numbers.

Least Common Multiple (LCM) of 31306 and 31312 is 490126736.

LCM(31306,31312) = 490126736

LCM of 31306 and 31312

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

LCM of:
and

Least Common Multiple of 31306 and 31312

LCM of 31306 and 31312 is 490126736

Least common multiple can be found by multiplying the highest exponent prime factors of 31306 and 31312. First we will calculate the prime factors of 31306 and 31312.

Prime Factorization of 31306


2 31306
11 15653
1423 1423
1

Prime factors of 31306 are 2, 11,1423. Prime factorization of 31306 in exponential form is:

31306 = 21×111×14231

Prime Factorization of 31312


2 31312
2 15656
2 7828
2 3914
19 1957
103 103
1

Prime factors of 31312 are 2, 19,103. Prime factorization of 31312 in exponential form is:

31312 = 24×191×1031

Now multiplying the highest exponent prime factors to calculate the LCM of 31306 and 31312.

LCM(31306,31312) = 24×111×191×1031×14231
LCM(31306,31312) = 490126736

Factors of 31306

List of positive integer factors of 31306 that divides 31306 without a remainder.

1, 2, 11, 22, 1423, 2846, 15653, 31306

Factors of 31312

List of positive integer factors of 31312 that divides 31312 without a remainder.

1, 2, 4, 8, 16, 19, 38, 76, 103, 152, 206, 304, 412, 824, 1648, 1957, 3914, 7828, 15656, 31312

Least Common Multiple of 31306 and 31312 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 31306 and 31312, than apply into the LCM equation.

GCF(31306,31312) = 2
LCM(31306,31312) = ( 31306 × 31312) / 2
LCM(31306,31312) = 980253472 / 2
LCM(31306,31312) = 490126736

Properties of LCM 31306 and 31312

(i) The LCM of 31312 and 31306 is associative

LCM of 31306 and 31312 = LCM of 31312 and 31306

Related Least Common Multiples of 31306

Related Least Common Multiples of 31312

Frequently Asked Questions on LCM of 31306 and 31312

1. What is the LCM of 31306 and 31312?

Answer: LCM of 31306 and 31312 is 490126736.

2. What are the Factors of 31306?

Answer: Factors of 31306 are 1, 2, 11, 22, 1423, 2846, 15653, 31306. There are 8 integers that are factors of 31306. The greatest factor of 31306 is 31306.

3. What are the Factors of 31312?

Answer: Factors of 31312 are 1, 2, 4, 8, 16, 19, 38, 76, 103, 152, 206, 304, 412, 824, 1648, 1957, 3914, 7828, 15656, 31312. There are 20 integers that are factors of 31312. The greatest factor of 31312 is 31312.

4. How to Find the LCM of 31306 and 31312?

Answer:

Least Common Multiple of 31306 and 31312 = 490126736

Step 1: Find the prime factorization of 31306

31306 = 2 x 11 x 1423

Step 2: Find the prime factorization of 31312

31312 = 2 x 2 x 2 x 2 x 19 x 103

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

LCM = 490126736 = 2 x 2 x 2 x 2 x 11 x 19 x 103 x 1423

Step 4: Therefore, the least common multiple of 31306 and 31312 is 490126736.