Least Common Multiple of 217 and 218

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 217 and 218 the smallest integer that is 47306 that is divisible by both numbers.

Least Common Multiple (LCM) of 217 and 218 is 47306.

LCM(217,218) = 47306

LCM of 217 and 218

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

LCM of:
and

Least Common Multiple of 217 and 218

LCM of 217 and 218 is 47306

Least common multiple can be found by multiplying the highest exponent prime factors of 217 and 218. First we will calculate the prime factors of 217 and 218.

Prime Factorization of 217


7 217
31 31
1

Prime factors of 217 are 7,31. Prime factorization of 217 in exponential form is:

217 = 71×311

Prime Factorization of 218


2 218
109 109
1

Prime factors of 218 are 2,109. Prime factorization of 218 in exponential form is:

218 = 21×1091

Now multiplying the highest exponent prime factors to calculate the LCM of 217 and 218.

LCM(217,218) = 21×71×311×1091
LCM(217,218) = 47306

Factors of 217

List of positive integer factors of 217 that divides 217 without a remainder.

1, 7, 31, 217

Factors of 218

List of positive integer factors of 218 that divides 218 without a remainder.

1, 2, 109, 218

Least Common Multiple of 217 and 218 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 217 and 218, than apply into the LCM equation.

GCF(217,218) = 1
LCM(217,218) = ( 217 × 218) / 1
LCM(217,218) = 47306 / 1
LCM(217,218) = 47306

Properties of LCM 217 and 218

(i) The LCM of 218 and 217 is associative

LCM of 217 and 218 = LCM of 218 and 217

Related Least Common Multiples of 217

Related Least Common Multiples of 218

Frequently Asked Questions on LCM of 217 and 218

1. What is the LCM of 217 and 218?

Answer: LCM of 217 and 218 is 47306.

2. What are the Factors of 217?

Answer: Factors of 217 are 1, 7, 31, 217. There are 4 integers that are factors of 217. The greatest factor of 217 is 217.

3. What are the Factors of 218?

Answer: Factors of 218 are 1, 2, 109, 218. There are 4 integers that are factors of 218. The greatest factor of 218 is 218.

4. How to Find the LCM of 217 and 218?

Answer:

Least Common Multiple of 217 and 218 = 47306

Step 1: Find the prime factorization of 217

217 = 7 x 31

Step 2: Find the prime factorization of 218

218 = 2 x 109

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

LCM = 47306 = 2 x 7 x 31 x 109

Step 4: Therefore, the least common multiple of 217 and 218 is 47306.