Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 10224 and 10228 the smallest integer that is 26142768 that is divisible by both numbers.
Least Common Multiple (LCM) of 10224 and 10228 is 26142768.
LCM(10224,10228) = 26142768
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 10224 and 10228. First we will calculate the prime factors of 10224 and 10228.
Prime Factorization of 10224
2 | 10224 |
2 | 5112 |
2 | 2556 |
2 | 1278 |
3 | 639 |
3 | 213 |
71 | 71 |
1 |
Prime factors of 10224 are 2, 3,71. Prime factorization of 10224 in exponential form is:
10224 = 24×32×711
Prime Factorization of 10228
2 | 10228 |
2 | 5114 |
2557 | 2557 |
1 |
Prime factors of 10228 are 2,2557. Prime factorization of 10228 in exponential form is:
10228 = 22×25571
Now multiplying the highest exponent prime factors to calculate the LCM of 10224 and 10228.
LCM(10224,10228) = 24×32×711×25571
LCM(10224,10228) = 26142768
Factors of 10224
List of positive integer factors of 10224 that divides 10224 without a remainder.
1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 71, 72, 142, 144, 213, 284, 426, 568, 639, 852, 1136, 1278, 1704, 2556, 3408, 5112, 10224
Factors of 10228
List of positive integer factors of 10228 that divides 10228 without a remainder.
1, 2, 4, 2557, 5114, 10228
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 10224 and 10228, than apply into the LCM equation.
GCF(10224,10228) = 4
LCM(10224,10228) = ( 10224 × 10228) / 4
LCM(10224,10228) = 104571072 / 4
LCM(10224,10228) = 26142768
(i) The LCM of 10228 and 10224 is associative
LCM of 10224 and 10228 = LCM of 10228 and 10224
1. What is the LCM of 10224 and 10228?
Answer: LCM of 10224 and 10228 is 26142768.
2. What are the Factors of 10224?
Answer: Factors of 10224 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 71, 72, 142, 144, 213, 284, 426, 568, 639, 852, 1136, 1278, 1704, 2556, 3408, 5112, 10224. There are 30 integers that are factors of 10224. The greatest factor of 10224 is 10224.
3. What are the Factors of 10228?
Answer: Factors of 10228 are 1, 2, 4, 2557, 5114, 10228. There are 6 integers that are factors of 10228. The greatest factor of 10228 is 10228.
4. How to Find the LCM of 10224 and 10228?
Answer:
Least Common Multiple of 10224 and 10228 = 26142768
Step 1: Find the prime factorization of 10224
10224 = 2 x 2 x 2 x 2 x 3 x 3 x 71
Step 2: Find the prime factorization of 10228
10228 = 2 x 2 x 2557
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 26142768 = 2 x 2 x 2 x 2 x 3 x 3 x 71 x 2557
Step 4: Therefore, the least common multiple of 10224 and 10228 is 26142768.