Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 1220 and 1228 the smallest integer that is 374540 that is divisible by both numbers.
Least Common Multiple (LCM) of 1220 and 1228 is 374540.
LCM(1220,1228) = 374540
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 1220 and 1228. First we will calculate the prime factors of 1220 and 1228.
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
Prime Factorization of 1228
2 | 1228 |
2 | 614 |
307 | 307 |
1 |
Prime factors of 1228 are 2,307. Prime factorization of 1228 in exponential form is:
1228 = 22×3071
Now multiplying the highest exponent prime factors to calculate the LCM of 1220 and 1228.
LCM(1220,1228) = 22×51×611×3071
LCM(1220,1228) = 374540
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
Factors of 1228
List of positive integer factors of 1228 that divides 1228 without a remainder.
1, 2, 4, 307, 614, 1228
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1220 and 1228, than apply into the LCM equation.
GCF(1220,1228) = 4
LCM(1220,1228) = ( 1220 × 1228) / 4
LCM(1220,1228) = 1498160 / 4
LCM(1220,1228) = 374540
(i) The LCM of 1228 and 1220 is associative
LCM of 1220 and 1228 = LCM of 1228 and 1220
1. What is the LCM of 1220 and 1228?
Answer: LCM of 1220 and 1228 is 374540.
2. 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.
3. What are the Factors of 1228?
Answer: Factors of 1228 are 1, 2, 4, 307, 614, 1228. There are 6 integers that are factors of 1228. The greatest factor of 1228 is 1228.
4. How to Find the LCM of 1220 and 1228?
Answer:
Least Common Multiple of 1220 and 1228 = 374540
Step 1: Find the prime factorization of 1220
1220 = 2 x 2 x 5 x 61
Step 2: Find the prime factorization of 1228
1228 = 2 x 2 x 307
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 374540 = 2 x 2 x 5 x 61 x 307
Step 4: Therefore, the least common multiple of 1220 and 1228 is 374540.