Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 4220 and 4224 the smallest integer that is 4456320 that is divisible by both numbers.
Least Common Multiple (LCM) of 4220 and 4224 is 4456320.
LCM(4220,4224) = 4456320
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 4220 and 4224. First we will calculate the prime factors of 4220 and 4224.
Prime Factorization of 4220
2 | 4220 |
2 | 2110 |
5 | 1055 |
211 | 211 |
1 |
Prime factors of 4220 are 2, 5,211. Prime factorization of 4220 in exponential form is:
4220 = 22×51×2111
Prime Factorization of 4224
2 | 4224 |
2 | 2112 |
2 | 1056 |
2 | 528 |
2 | 264 |
2 | 132 |
2 | 66 |
3 | 33 |
11 | 11 |
1 |
Prime factors of 4224 are 2, 3,11. Prime factorization of 4224 in exponential form is:
4224 = 27×31×111
Now multiplying the highest exponent prime factors to calculate the LCM of 4220 and 4224.
LCM(4220,4224) = 27×31×51×111×2111
LCM(4220,4224) = 4456320
Factors of 4220
List of positive integer factors of 4220 that divides 4220 without a remainder.
1, 2, 4, 5, 10, 20, 211, 422, 844, 1055, 2110, 4220
Factors of 4224
List of positive integer factors of 4224 that divides 4224 without a remainder.
1, 2, 3, 4, 6, 8, 11, 12, 16, 22, 24, 32, 33, 44, 48, 64, 66, 88, 96, 128, 132, 176, 192, 264, 352, 384, 528, 704, 1056, 1408, 2112, 4224
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 4220 and 4224, than apply into the LCM equation.
GCF(4220,4224) = 4
LCM(4220,4224) = ( 4220 × 4224) / 4
LCM(4220,4224) = 17825280 / 4
LCM(4220,4224) = 4456320
(i) The LCM of 4224 and 4220 is associative
LCM of 4220 and 4224 = LCM of 4224 and 4220
1. What is the LCM of 4220 and 4224?
Answer: LCM of 4220 and 4224 is 4456320.
2. What are the Factors of 4220?
Answer: Factors of 4220 are 1, 2, 4, 5, 10, 20, 211, 422, 844, 1055, 2110, 4220. There are 12 integers that are factors of 4220. The greatest factor of 4220 is 4220.
3. What are the Factors of 4224?
Answer: Factors of 4224 are 1, 2, 3, 4, 6, 8, 11, 12, 16, 22, 24, 32, 33, 44, 48, 64, 66, 88, 96, 128, 132, 176, 192, 264, 352, 384, 528, 704, 1056, 1408, 2112, 4224. There are 32 integers that are factors of 4224. The greatest factor of 4224 is 4224.
4. How to Find the LCM of 4220 and 4224?
Answer:
Least Common Multiple of 4220 and 4224 = 4456320
Step 1: Find the prime factorization of 4220
4220 = 2 x 2 x 5 x 211
Step 2: Find the prime factorization of 4224
4224 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 x 11
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 4456320 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 x 5 x 11 x 211
Step 4: Therefore, the least common multiple of 4220 and 4224 is 4456320.