Least Common Multiple of 219 and 220

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 219 and 220 the smallest integer that is 48180 that is divisible by both numbers.

Least Common Multiple (LCM) of 219 and 220 is 48180.

LCM(219,220) = 48180

LCM of 219 and 220

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

LCM of:
and

Least Common Multiple of 219 and 220

LCM of 219 and 220 is 48180

Least common multiple can be found by multiplying the highest exponent prime factors of 219 and 220. First we will calculate the prime factors of 219 and 220.

Prime Factorization of 219


3 219
73 73
1

Prime factors of 219 are 3,73. Prime factorization of 219 in exponential form is:

219 = 31×731

Prime Factorization of 220


2 220
2 110
5 55
11 11
1

Prime factors of 220 are 2, 5,11. Prime factorization of 220 in exponential form is:

220 = 22×51×111

Now multiplying the highest exponent prime factors to calculate the LCM of 219 and 220.

LCM(219,220) = 22×31×51×111×731
LCM(219,220) = 48180

Factors of 219

List of positive integer factors of 219 that divides 219 without a remainder.

1, 3, 73, 219

Factors of 220

List of positive integer factors of 220 that divides 220 without a remainder.

1, 2, 4, 5, 10, 11, 20, 22, 44, 55, 110, 220

Least Common Multiple of 219 and 220 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 219 and 220, than apply into the LCM equation.

GCF(219,220) = 1
LCM(219,220) = ( 219 × 220) / 1
LCM(219,220) = 48180 / 1
LCM(219,220) = 48180

Properties of LCM 219 and 220

(i) The LCM of 220 and 219 is associative

LCM of 219 and 220 = LCM of 220 and 219

Related Least Common Multiples of 219

Related Least Common Multiples of 220

Frequently Asked Questions on LCM of 219 and 220

1. What is the LCM of 219 and 220?

Answer: LCM of 219 and 220 is 48180.

2. What are the Factors of 219?

Answer: Factors of 219 are 1, 3, 73, 219. There are 4 integers that are factors of 219. The greatest factor of 219 is 219.

3. What are the Factors of 220?

Answer: Factors of 220 are 1, 2, 4, 5, 10, 11, 20, 22, 44, 55, 110, 220. There are 12 integers that are factors of 220. The greatest factor of 220 is 220.

4. How to Find the LCM of 219 and 220?

Answer:

Least Common Multiple of 219 and 220 = 48180

Step 1: Find the prime factorization of 219

219 = 3 x 73

Step 2: Find the prime factorization of 220

220 = 2 x 2 x 5 x 11

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

LCM = 48180 = 2 x 2 x 3 x 5 x 11 x 73

Step 4: Therefore, the least common multiple of 219 and 220 is 48180.