Least Common Multiple of 7314 and 7320

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 7314 and 7320 the smallest integer that is 8923080 that is divisible by both numbers.

Least Common Multiple (LCM) of 7314 and 7320 is 8923080.

LCM(7314,7320) = 8923080

LCM of 7314 and 7320

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

LCM of:
and

Least Common Multiple of 7314 and 7320

LCM of 7314 and 7320 is 8923080

Least common multiple can be found by multiplying the highest exponent prime factors of 7314 and 7320. First we will calculate the prime factors of 7314 and 7320.

Prime Factorization of 7314


2 7314
3 3657
23 1219
53 53
1

Prime factors of 7314 are 2, 3, 23,53. Prime factorization of 7314 in exponential form is:

7314 = 21×31×231×531

Prime Factorization of 7320


2 7320
2 3660
2 1830
3 915
5 305
61 61
1

Prime factors of 7320 are 2, 3, 5,61. Prime factorization of 7320 in exponential form is:

7320 = 23×31×51×611

Now multiplying the highest exponent prime factors to calculate the LCM of 7314 and 7320.

LCM(7314,7320) = 23×31×51×231×531×611
LCM(7314,7320) = 8923080

Factors of 7314

List of positive integer factors of 7314 that divides 7314 without a remainder.

1, 2, 3, 6, 23, 46, 53, 69, 106, 138, 159, 318, 1219, 2438, 3657, 7314

Factors of 7320

List of positive integer factors of 7320 that divides 7320 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 61, 120, 122, 183, 244, 305, 366, 488, 610, 732, 915, 1220, 1464, 1830, 2440, 3660, 7320

Least Common Multiple of 7314 and 7320 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 7314 and 7320, than apply into the LCM equation.

GCF(7314,7320) = 6
LCM(7314,7320) = ( 7314 × 7320) / 6
LCM(7314,7320) = 53538480 / 6
LCM(7314,7320) = 8923080

Properties of LCM 7314 and 7320

(i) The LCM of 7320 and 7314 is associative

LCM of 7314 and 7320 = LCM of 7320 and 7314

Related Least Common Multiples of 7314

Related Least Common Multiples of 7320

Frequently Asked Questions on LCM of 7314 and 7320

1. What is the LCM of 7314 and 7320?

Answer: LCM of 7314 and 7320 is 8923080.

2. What are the Factors of 7314?

Answer: Factors of 7314 are 1, 2, 3, 6, 23, 46, 53, 69, 106, 138, 159, 318, 1219, 2438, 3657, 7314. There are 16 integers that are factors of 7314. The greatest factor of 7314 is 7314.

3. What are the Factors of 7320?

Answer: Factors of 7320 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 61, 120, 122, 183, 244, 305, 366, 488, 610, 732, 915, 1220, 1464, 1830, 2440, 3660, 7320. There are 32 integers that are factors of 7320. The greatest factor of 7320 is 7320.

4. How to Find the LCM of 7314 and 7320?

Answer:

Least Common Multiple of 7314 and 7320 = 8923080

Step 1: Find the prime factorization of 7314

7314 = 2 x 3 x 23 x 53

Step 2: Find the prime factorization of 7320

7320 = 2 x 2 x 2 x 3 x 5 x 61

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

LCM = 8923080 = 2 x 2 x 2 x 3 x 5 x 23 x 53 x 61

Step 4: Therefore, the least common multiple of 7314 and 7320 is 8923080.