Least Common Multiple of 185 and 192

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 185 and 192 the smallest integer that is 35520 that is divisible by both numbers.

Least Common Multiple (LCM) of 185 and 192 is 35520.

LCM(185,192) = 35520

LCM of 185 and 192

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

LCM of:
and

Least Common Multiple of 185 and 192

LCM of 185 and 192 is 35520

Least common multiple can be found by multiplying the highest exponent prime factors of 185 and 192. First we will calculate the prime factors of 185 and 192.

Prime Factorization of 185


5 185
37 37
1

Prime factors of 185 are 5,37. Prime factorization of 185 in exponential form is:

185 = 51×371

Prime Factorization of 192


2 192
2 96
2 48
2 24
2 12
2 6
3 3
1

Prime factors of 192 are 2,3. Prime factorization of 192 in exponential form is:

192 = 26×31

Now multiplying the highest exponent prime factors to calculate the LCM of 185 and 192.

LCM(185,192) = 26×31×51×371
LCM(185,192) = 35520

Factors of 185

List of positive integer factors of 185 that divides 185 without a remainder.

1, 5, 37, 185

Factors of 192

List of positive integer factors of 192 that divides 192 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 192

Least Common Multiple of 185 and 192 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 185 and 192, than apply into the LCM equation.

GCF(185,192) = 1
LCM(185,192) = ( 185 × 192) / 1
LCM(185,192) = 35520 / 1
LCM(185,192) = 35520

Properties of LCM 185 and 192

(i) The LCM of 192 and 185 is associative

LCM of 185 and 192 = LCM of 192 and 185

Related Least Common Multiples of 185

Related Least Common Multiples of 192

Frequently Asked Questions on LCM of 185 and 192

1. What is the LCM of 185 and 192?

Answer: LCM of 185 and 192 is 35520.

2. What are the Factors of 185?

Answer: Factors of 185 are 1, 5, 37, 185. There are 4 integers that are factors of 185. The greatest factor of 185 is 185.

3. What are the Factors of 192?

Answer: Factors of 192 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 192. There are 14 integers that are factors of 192. The greatest factor of 192 is 192.

4. How to Find the LCM of 185 and 192?

Answer:

Least Common Multiple of 185 and 192 = 35520

Step 1: Find the prime factorization of 185

185 = 5 x 37

Step 2: Find the prime factorization of 192

192 = 2 x 2 x 2 x 2 x 2 x 2 x 3

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

LCM = 35520 = 2 x 2 x 2 x 2 x 2 x 2 x 3 x 5 x 37

Step 4: Therefore, the least common multiple of 185 and 192 is 35520.