Least Common Multiple of 7305 and 7312

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 7305 and 7312 the smallest integer that is 53414160 that is divisible by both numbers.

Least Common Multiple (LCM) of 7305 and 7312 is 53414160.

LCM(7305,7312) = 53414160

LCM of 7305 and 7312

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

LCM of:
and

Least Common Multiple of 7305 and 7312

LCM of 7305 and 7312 is 53414160

Least common multiple can be found by multiplying the highest exponent prime factors of 7305 and 7312. First we will calculate the prime factors of 7305 and 7312.

Prime Factorization of 7305


3 7305
5 2435
487 487
1

Prime factors of 7305 are 3, 5,487. Prime factorization of 7305 in exponential form is:

7305 = 31×51×4871

Prime Factorization of 7312


2 7312
2 3656
2 1828
2 914
457 457
1

Prime factors of 7312 are 2,457. Prime factorization of 7312 in exponential form is:

7312 = 24×4571

Now multiplying the highest exponent prime factors to calculate the LCM of 7305 and 7312.

LCM(7305,7312) = 24×31×51×4571×4871
LCM(7305,7312) = 53414160

Factors of 7305

List of positive integer factors of 7305 that divides 7305 without a remainder.

1, 3, 5, 15, 487, 1461, 2435, 7305

Factors of 7312

List of positive integer factors of 7312 that divides 7312 without a remainder.

1, 2, 4, 8, 16, 457, 914, 1828, 3656, 7312

Least Common Multiple of 7305 and 7312 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 7305 and 7312, than apply into the LCM equation.

GCF(7305,7312) = 1
LCM(7305,7312) = ( 7305 × 7312) / 1
LCM(7305,7312) = 53414160 / 1
LCM(7305,7312) = 53414160

Properties of LCM 7305 and 7312

(i) The LCM of 7312 and 7305 is associative

LCM of 7305 and 7312 = LCM of 7312 and 7305

Related Least Common Multiples of 7305

Related Least Common Multiples of 7312

Frequently Asked Questions on LCM of 7305 and 7312

1. What is the LCM of 7305 and 7312?

Answer: LCM of 7305 and 7312 is 53414160.

2. What are the Factors of 7305?

Answer: Factors of 7305 are 1, 3, 5, 15, 487, 1461, 2435, 7305. There are 8 integers that are factors of 7305. The greatest factor of 7305 is 7305.

3. What are the Factors of 7312?

Answer: Factors of 7312 are 1, 2, 4, 8, 16, 457, 914, 1828, 3656, 7312. There are 10 integers that are factors of 7312. The greatest factor of 7312 is 7312.

4. How to Find the LCM of 7305 and 7312?

Answer:

Least Common Multiple of 7305 and 7312 = 53414160

Step 1: Find the prime factorization of 7305

7305 = 3 x 5 x 487

Step 2: Find the prime factorization of 7312

7312 = 2 x 2 x 2 x 2 x 457

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

LCM = 53414160 = 2 x 2 x 2 x 2 x 3 x 5 x 457 x 487

Step 4: Therefore, the least common multiple of 7305 and 7312 is 53414160.