Least Common Multiple of 31312 and 31314

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 31312 and 31314 the smallest integer that is 490251984 that is divisible by both numbers.

Least Common Multiple (LCM) of 31312 and 31314 is 490251984.

LCM(31312,31314) = 490251984

LCM of 31312 and 31314

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

LCM of:
and

Least Common Multiple of 31312 and 31314

LCM of 31312 and 31314 is 490251984

Least common multiple can be found by multiplying the highest exponent prime factors of 31312 and 31314. First we will calculate the prime factors of 31312 and 31314.

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

Prime Factorization of 31314


2 31314
3 15657
17 5219
307 307
1

Prime factors of 31314 are 2, 3, 17,307. Prime factorization of 31314 in exponential form is:

31314 = 21×31×171×3071

Now multiplying the highest exponent prime factors to calculate the LCM of 31312 and 31314.

LCM(31312,31314) = 24×31×171×191×1031×3071
LCM(31312,31314) = 490251984

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

Factors of 31314

List of positive integer factors of 31314 that divides 31314 without a remainder.

1, 2, 3, 6, 17, 34, 51, 102, 307, 614, 921, 1842, 5219, 10438, 15657, 31314

Least Common Multiple of 31312 and 31314 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 31312 and 31314, than apply into the LCM equation.

GCF(31312,31314) = 2
LCM(31312,31314) = ( 31312 × 31314) / 2
LCM(31312,31314) = 980503968 / 2
LCM(31312,31314) = 490251984

Properties of LCM 31312 and 31314

(i) The LCM of 31314 and 31312 is associative

LCM of 31312 and 31314 = LCM of 31314 and 31312

Related Least Common Multiples of 31312

Related Least Common Multiples of 31314

Frequently Asked Questions on LCM of 31312 and 31314

1. What is the LCM of 31312 and 31314?

Answer: LCM of 31312 and 31314 is 490251984.

2. 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.

3. What are the Factors of 31314?

Answer: Factors of 31314 are 1, 2, 3, 6, 17, 34, 51, 102, 307, 614, 921, 1842, 5219, 10438, 15657, 31314. There are 16 integers that are factors of 31314. The greatest factor of 31314 is 31314.

4. How to Find the LCM of 31312 and 31314?

Answer:

Least Common Multiple of 31312 and 31314 = 490251984

Step 1: Find the prime factorization of 31312

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

Step 2: Find the prime factorization of 31314

31314 = 2 x 3 x 17 x 307

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

LCM = 490251984 = 2 x 2 x 2 x 2 x 3 x 17 x 19 x 103 x 307

Step 4: Therefore, the least common multiple of 31312 and 31314 is 490251984.