Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 1215 and 1220 the smallest integer that is 296460 that is divisible by both numbers.
Least Common Multiple (LCM) of 1215 and 1220 is 296460.
LCM(1215,1220) = 296460
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 1215 and 1220. First we will calculate the prime factors of 1215 and 1220.
Prime Factorization of 1215
3 | 1215 |
3 | 405 |
3 | 135 |
3 | 45 |
3 | 15 |
5 | 5 |
1 |
Prime factors of 1215 are 3,5. Prime factorization of 1215 in exponential form is:
1215 = 35×51
Prime Factorization of 1220
2 | 1220 |
2 | 610 |
5 | 305 |
61 | 61 |
1 |
Prime factors of 1220 are 2, 5,61. Prime factorization of 1220 in exponential form is:
1220 = 22×51×611
Now multiplying the highest exponent prime factors to calculate the LCM of 1215 and 1220.
LCM(1215,1220) = 22×35×51×611
LCM(1215,1220) = 296460
Factors of 1215
List of positive integer factors of 1215 that divides 1215 without a remainder.
1, 3, 5, 9, 15, 27, 45, 81, 135, 243, 405, 1215
Factors of 1220
List of positive integer factors of 1220 that divides 1220 without a remainder.
1, 2, 4, 5, 10, 20, 61, 122, 244, 305, 610, 1220
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1215 and 1220, than apply into the LCM equation.
GCF(1215,1220) = 5
LCM(1215,1220) = ( 1215 × 1220) / 5
LCM(1215,1220) = 1482300 / 5
LCM(1215,1220) = 296460
(i) The LCM of 1220 and 1215 is associative
LCM of 1215 and 1220 = LCM of 1220 and 1215
1. What is the LCM of 1215 and 1220?
Answer: LCM of 1215 and 1220 is 296460.
2. What are the Factors of 1215?
Answer: Factors of 1215 are 1, 3, 5, 9, 15, 27, 45, 81, 135, 243, 405, 1215. There are 12 integers that are factors of 1215. The greatest factor of 1215 is 1215.
3. What are the Factors of 1220?
Answer: Factors of 1220 are 1, 2, 4, 5, 10, 20, 61, 122, 244, 305, 610, 1220. There are 12 integers that are factors of 1220. The greatest factor of 1220 is 1220.
4. How to Find the LCM of 1215 and 1220?
Answer:
Least Common Multiple of 1215 and 1220 = 296460
Step 1: Find the prime factorization of 1215
1215 = 3 x 3 x 3 x 3 x 3 x 5
Step 2: Find the prime factorization of 1220
1220 = 2 x 2 x 5 x 61
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 296460 = 2 x 2 x 3 x 3 x 3 x 3 x 3 x 5 x 61
Step 4: Therefore, the least common multiple of 1215 and 1220 is 296460.