Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 8728 and 8736 the smallest integer that is 9530976 that is divisible by both numbers.
Least Common Multiple (LCM) of 8728 and 8736 is 9530976.
LCM(8728,8736) = 9530976
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 8728 and 8736. First we will calculate the prime factors of 8728 and 8736.
Prime Factorization of 8728
2 | 8728 |
2 | 4364 |
2 | 2182 |
1091 | 1091 |
1 |
Prime factors of 8728 are 2,1091. Prime factorization of 8728 in exponential form is:
8728 = 23×10911
Prime Factorization of 8736
2 | 8736 |
2 | 4368 |
2 | 2184 |
2 | 1092 |
2 | 546 |
3 | 273 |
7 | 91 |
13 | 13 |
1 |
Prime factors of 8736 are 2, 3, 7,13. Prime factorization of 8736 in exponential form is:
8736 = 25×31×71×131
Now multiplying the highest exponent prime factors to calculate the LCM of 8728 and 8736.
LCM(8728,8736) = 25×31×71×131×10911
LCM(8728,8736) = 9530976
Factors of 8728
List of positive integer factors of 8728 that divides 8728 without a remainder.
1, 2, 4, 8, 1091, 2182, 4364, 8728
Factors of 8736
List of positive integer factors of 8736 that divides 8736 without a remainder.
1, 2, 3, 4, 6, 7, 8, 12, 13, 14, 16, 21, 24, 26, 28, 32, 39, 42, 48, 52, 56, 78, 84, 91, 96, 104, 112, 156, 168, 182, 208, 224, 273, 312, 336, 364, 416, 546, 624, 672, 728, 1092, 1248, 1456, 2184, 2912, 4368, 8736
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 8728 and 8736, than apply into the LCM equation.
GCF(8728,8736) = 8
LCM(8728,8736) = ( 8728 × 8736) / 8
LCM(8728,8736) = 76247808 / 8
LCM(8728,8736) = 9530976
(i) The LCM of 8736 and 8728 is associative
LCM of 8728 and 8736 = LCM of 8736 and 8728
1. What is the LCM of 8728 and 8736?
Answer: LCM of 8728 and 8736 is 9530976.
2. What are the Factors of 8728?
Answer: Factors of 8728 are 1, 2, 4, 8, 1091, 2182, 4364, 8728. There are 8 integers that are factors of 8728. The greatest factor of 8728 is 8728.
3. What are the Factors of 8736?
Answer: Factors of 8736 are 1, 2, 3, 4, 6, 7, 8, 12, 13, 14, 16, 21, 24, 26, 28, 32, 39, 42, 48, 52, 56, 78, 84, 91, 96, 104, 112, 156, 168, 182, 208, 224, 273, 312, 336, 364, 416, 546, 624, 672, 728, 1092, 1248, 1456, 2184, 2912, 4368, 8736. There are 48 integers that are factors of 8736. The greatest factor of 8736 is 8736.
4. How to Find the LCM of 8728 and 8736?
Answer:
Least Common Multiple of 8728 and 8736 = 9530976
Step 1: Find the prime factorization of 8728
8728 = 2 x 2 x 2 x 1091
Step 2: Find the prime factorization of 8736
8736 = 2 x 2 x 2 x 2 x 2 x 3 x 7 x 13
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 9530976 = 2 x 2 x 2 x 2 x 2 x 3 x 7 x 13 x 1091
Step 4: Therefore, the least common multiple of 8728 and 8736 is 9530976.