Least Common Multiple of 304 and 305

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 304 and 305 the smallest integer that is 92720 that is divisible by both numbers.

Least Common Multiple (LCM) of 304 and 305 is 92720.

LCM(304,305) = 92720

LCM of 304 and 305

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

LCM of:
and

Least Common Multiple of 304 and 305

LCM of 304 and 305 is 92720

Least common multiple can be found by multiplying the highest exponent prime factors of 304 and 305. First we will calculate the prime factors of 304 and 305.

Prime Factorization of 304


2 304
2 152
2 76
2 38
19 19
1

Prime factors of 304 are 2,19. Prime factorization of 304 in exponential form is:

304 = 24×191

Prime Factorization of 305


5 305
61 61
1

Prime factors of 305 are 5,61. Prime factorization of 305 in exponential form is:

305 = 51×611

Now multiplying the highest exponent prime factors to calculate the LCM of 304 and 305.

LCM(304,305) = 24×51×191×611
LCM(304,305) = 92720

Factors of 304

List of positive integer factors of 304 that divides 304 without a remainder.

1, 2, 4, 8, 16, 19, 38, 76, 152, 304

Factors of 305

List of positive integer factors of 305 that divides 305 without a remainder.

1, 5, 61, 305

Least Common Multiple of 304 and 305 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 304 and 305, than apply into the LCM equation.

GCF(304,305) = 1
LCM(304,305) = ( 304 × 305) / 1
LCM(304,305) = 92720 / 1
LCM(304,305) = 92720

Properties of LCM 304 and 305

(i) The LCM of 305 and 304 is associative

LCM of 304 and 305 = LCM of 305 and 304

Related Least Common Multiples of 304

Related Least Common Multiples of 305

Frequently Asked Questions on LCM of 304 and 305

1. What is the LCM of 304 and 305?

Answer: LCM of 304 and 305 is 92720.

2. What are the Factors of 304?

Answer: Factors of 304 are 1, 2, 4, 8, 16, 19, 38, 76, 152, 304. There are 10 integers that are factors of 304. The greatest factor of 304 is 304.

3. What are the Factors of 305?

Answer: Factors of 305 are 1, 5, 61, 305. There are 4 integers that are factors of 305. The greatest factor of 305 is 305.

4. How to Find the LCM of 304 and 305?

Answer:

Least Common Multiple of 304 and 305 = 92720

Step 1: Find the prime factorization of 304

304 = 2 x 2 x 2 x 2 x 19

Step 2: Find the prime factorization of 305

305 = 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 = 92720 = 2 x 2 x 2 x 2 x 5 x 19 x 61

Step 4: Therefore, the least common multiple of 304 and 305 is 92720.