Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 221 and 225 the smallest integer that is 49725 that is divisible by both numbers.
Least Common Multiple (LCM) of 221 and 225 is 49725.
LCM(221,225) = 49725
Least common multiple or lowest common denominator (LCD) can be calculated in three ways;
Least common multiple can be found by multiplying the highest exponent prime factors of 221 and 225. First we will calculate the prime factors of 221 and 225.
Prime Factorization of 221
13 | 221 |
17 | 17 |
1 |
Prime factors of 221 are 13,17. Prime factorization of 221 in exponential form is:
221 = 131×171
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 221 and 225.
LCM(221,225) = 32×52×131×171
LCM(221,225) = 49725
Factors of 221
List of positive integer factors of 221 that divides 221 without a remainder.
1, 13, 17, 221
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
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 221 and 225, than apply into the LCM equation.
GCF(221,225) = 1
LCM(221,225) = ( 221 × 225) / 1
LCM(221,225) = 49725 / 1
LCM(221,225) = 49725
(i) The LCM of 225 and 221 is associative
LCM of 221 and 225 = LCM of 225 and 221
1. What is the LCM of 221 and 225?
Answer: LCM of 221 and 225 is 49725.
2. What are the Factors of 221?
Answer: Factors of 221 are 1, 13, 17, 221. There are 4 integers that are factors of 221. The greatest factor of 221 is 221.
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 221 and 225?
Answer:
Least Common Multiple of 221 and 225 = 49725
Step 1: Find the prime factorization of 221
221 = 13 x 17
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 = 49725 = 3 x 3 x 5 x 5 x 13 x 17
Step 4: Therefore, the least common multiple of 221 and 225 is 49725.