Least Common Multiple of 217 and 225

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 225 the smallest integer that is 48825 that is divisible by both numbers.

Least Common Multiple (LCM) of 217 and 225 is 48825.

LCM(217,225) = 48825

LCM of 217 and 225

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

LCM of:
and

Least Common Multiple of 217 and 225

LCM of 217 and 225 is 48825

Least common multiple can be found by multiplying the highest exponent prime factors of 217 and 225. First we will calculate the prime factors of 217 and 225.

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 225


3 225
3 75
5 25
5 5
1

Prime factors of 225 are 3,5. Prime factorization of 225 in exponential form is:

225 = 32×52

Now multiplying the highest exponent prime factors to calculate the LCM of 217 and 225.

LCM(217,225) = 32×52×71×311
LCM(217,225) = 48825

Factors of 217

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

1, 7, 31, 217

Factors of 225

List of positive integer factors of 225 that divides 225 without a remainder.

1, 3, 5, 9, 15, 25, 45, 75, 225

Least Common Multiple of 217 and 225 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 225, than apply into the LCM equation.

GCF(217,225) = 1
LCM(217,225) = ( 217 × 225) / 1
LCM(217,225) = 48825 / 1
LCM(217,225) = 48825

Properties of LCM 217 and 225

(i) The LCM of 225 and 217 is associative

LCM of 217 and 225 = LCM of 225 and 217

Related Least Common Multiples of 217

Related Least Common Multiples of 225

Frequently Asked Questions on LCM of 217 and 225

1. What is the LCM of 217 and 225?

Answer: LCM of 217 and 225 is 48825.

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 225?

Answer: Factors of 225 are 1, 3, 5, 9, 15, 25, 45, 75, 225. There are 9 integers that are factors of 225. The greatest factor of 225 is 225.

4. How to Find the LCM of 217 and 225?

Answer:

Least Common Multiple of 217 and 225 = 48825

Step 1: Find the prime factorization of 217

217 = 7 x 31

Step 2: Find the prime factorization of 225

225 = 3 x 3 x 5 x 5

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

LCM = 48825 = 3 x 3 x 5 x 5 x 7 x 31

Step 4: Therefore, the least common multiple of 217 and 225 is 48825.