Least Common Multiple of 31312 and 31320

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 31320 the smallest integer that is 122586480 that is divisible by both numbers.

Least Common Multiple (LCM) of 31312 and 31320 is 122586480.

LCM(31312,31320) = 122586480

LCM of 31312 and 31320

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

LCM of:
and

Least Common Multiple of 31312 and 31320

LCM of 31312 and 31320 is 122586480

Least common multiple can be found by multiplying the highest exponent prime factors of 31312 and 31320. First we will calculate the prime factors of 31312 and 31320.

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 31320


2 31320
2 15660
2 7830
3 3915
3 1305
3 435
5 145
29 29
1

Prime factors of 31320 are 2, 3, 5,29. Prime factorization of 31320 in exponential form is:

31320 = 23×33×51×291

Now multiplying the highest exponent prime factors to calculate the LCM of 31312 and 31320.

LCM(31312,31320) = 24×33×51×191×291×1031
LCM(31312,31320) = 122586480

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 31320

List of positive integer factors of 31320 that divides 31320 without a remainder.

1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 27, 29, 30, 36, 40, 45, 54, 58, 60, 72, 87, 90, 108, 116, 120, 135, 145, 174, 180, 216, 232, 261, 270, 290, 348, 360, 435, 522, 540, 580, 696, 783, 870, 1044, 1080, 1160, 1305, 1566, 1740, 2088, 2610, 3132, 3480, 3915, 5220, 6264, 7830, 10440, 15660, 31320

Least Common Multiple of 31312 and 31320 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 31320, than apply into the LCM equation.

GCF(31312,31320) = 8
LCM(31312,31320) = ( 31312 × 31320) / 8
LCM(31312,31320) = 980691840 / 8
LCM(31312,31320) = 122586480

Properties of LCM 31312 and 31320

(i) The LCM of 31320 and 31312 is associative

LCM of 31312 and 31320 = LCM of 31320 and 31312

Related Least Common Multiples of 31312

Related Least Common Multiples of 31320

Frequently Asked Questions on LCM of 31312 and 31320

1. What is the LCM of 31312 and 31320?

Answer: LCM of 31312 and 31320 is 122586480.

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 31320?

Answer: Factors of 31320 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 27, 29, 30, 36, 40, 45, 54, 58, 60, 72, 87, 90, 108, 116, 120, 135, 145, 174, 180, 216, 232, 261, 270, 290, 348, 360, 435, 522, 540, 580, 696, 783, 870, 1044, 1080, 1160, 1305, 1566, 1740, 2088, 2610, 3132, 3480, 3915, 5220, 6264, 7830, 10440, 15660, 31320. There are 64 integers that are factors of 31320. The greatest factor of 31320 is 31320.

4. How to Find the LCM of 31312 and 31320?

Answer:

Least Common Multiple of 31312 and 31320 = 122586480

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 31320

31320 = 2 x 2 x 2 x 3 x 3 x 3 x 5 x 29

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

LCM = 122586480 = 2 x 2 x 2 x 2 x 3 x 3 x 3 x 5 x 19 x 29 x 103

Step 4: Therefore, the least common multiple of 31312 and 31320 is 122586480.