Least Common Multiple of 10314 and 10320

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 10314 and 10320 the smallest integer that is 17740080 that is divisible by both numbers.

Least Common Multiple (LCM) of 10314 and 10320 is 17740080.

LCM(10314,10320) = 17740080

LCM of 10314 and 10320

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

LCM of:
and

Least Common Multiple of 10314 and 10320

LCM of 10314 and 10320 is 17740080

Least common multiple can be found by multiplying the highest exponent prime factors of 10314 and 10320. First we will calculate the prime factors of 10314 and 10320.

Prime Factorization of 10314


2 10314
3 5157
3 1719
3 573
191 191
1

Prime factors of 10314 are 2, 3,191. Prime factorization of 10314 in exponential form is:

10314 = 21×33×1911

Prime Factorization of 10320


2 10320
2 5160
2 2580
2 1290
3 645
5 215
43 43
1

Prime factors of 10320 are 2, 3, 5,43. Prime factorization of 10320 in exponential form is:

10320 = 24×31×51×431

Now multiplying the highest exponent prime factors to calculate the LCM of 10314 and 10320.

LCM(10314,10320) = 24×33×51×431×1911
LCM(10314,10320) = 17740080

Factors of 10314

List of positive integer factors of 10314 that divides 10314 without a remainder.

1, 2, 3, 6, 9, 18, 27, 54, 191, 382, 573, 1146, 1719, 3438, 5157, 10314

Factors of 10320

List of positive integer factors of 10320 that divides 10320 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 43, 48, 60, 80, 86, 120, 129, 172, 215, 240, 258, 344, 430, 516, 645, 688, 860, 1032, 1290, 1720, 2064, 2580, 3440, 5160, 10320

Least Common Multiple of 10314 and 10320 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 10314 and 10320, than apply into the LCM equation.

GCF(10314,10320) = 6
LCM(10314,10320) = ( 10314 × 10320) / 6
LCM(10314,10320) = 106440480 / 6
LCM(10314,10320) = 17740080

Properties of LCM 10314 and 10320

(i) The LCM of 10320 and 10314 is associative

LCM of 10314 and 10320 = LCM of 10320 and 10314

Related Least Common Multiples of 10314

Related Least Common Multiples of 10320

Frequently Asked Questions on LCM of 10314 and 10320

1. What is the LCM of 10314 and 10320?

Answer: LCM of 10314 and 10320 is 17740080.

2. What are the Factors of 10314?

Answer: Factors of 10314 are 1, 2, 3, 6, 9, 18, 27, 54, 191, 382, 573, 1146, 1719, 3438, 5157, 10314. There are 16 integers that are factors of 10314. The greatest factor of 10314 is 10314.

3. What are the Factors of 10320?

Answer: Factors of 10320 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 43, 48, 60, 80, 86, 120, 129, 172, 215, 240, 258, 344, 430, 516, 645, 688, 860, 1032, 1290, 1720, 2064, 2580, 3440, 5160, 10320. There are 40 integers that are factors of 10320. The greatest factor of 10320 is 10320.

4. How to Find the LCM of 10314 and 10320?

Answer:

Least Common Multiple of 10314 and 10320 = 17740080

Step 1: Find the prime factorization of 10314

10314 = 2 x 3 x 3 x 3 x 191

Step 2: Find the prime factorization of 10320

10320 = 2 x 2 x 2 x 2 x 3 x 5 x 43

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

LCM = 17740080 = 2 x 2 x 2 x 2 x 3 x 3 x 3 x 5 x 43 x 191

Step 4: Therefore, the least common multiple of 10314 and 10320 is 17740080.