Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 8755 and 8760 the smallest integer that is 15338760 that is divisible by both numbers.
Least Common Multiple (LCM) of 8755 and 8760 is 15338760.
LCM(8755,8760) = 15338760
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 8755 and 8760. First we will calculate the prime factors of 8755 and 8760.
Prime Factorization of 8755
5 | 8755 |
17 | 1751 |
103 | 103 |
1 |
Prime factors of 8755 are 5, 17,103. Prime factorization of 8755 in exponential form is:
8755 = 51×171×1031
Prime Factorization of 8760
2 | 8760 |
2 | 4380 |
2 | 2190 |
3 | 1095 |
5 | 365 |
73 | 73 |
1 |
Prime factors of 8760 are 2, 3, 5,73. Prime factorization of 8760 in exponential form is:
8760 = 23×31×51×731
Now multiplying the highest exponent prime factors to calculate the LCM of 8755 and 8760.
LCM(8755,8760) = 23×31×51×171×731×1031
LCM(8755,8760) = 15338760
Factors of 8755
List of positive integer factors of 8755 that divides 8755 without a remainder.
1, 5, 17, 85, 103, 515, 1751, 8755
Factors of 8760
List of positive integer factors of 8760 that divides 8760 without a remainder.
1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 73, 120, 146, 219, 292, 365, 438, 584, 730, 876, 1095, 1460, 1752, 2190, 2920, 4380, 8760
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 8755 and 8760, than apply into the LCM equation.
GCF(8755,8760) = 5
LCM(8755,8760) = ( 8755 × 8760) / 5
LCM(8755,8760) = 76693800 / 5
LCM(8755,8760) = 15338760
(i) The LCM of 8760 and 8755 is associative
LCM of 8755 and 8760 = LCM of 8760 and 8755
1. What is the LCM of 8755 and 8760?
Answer: LCM of 8755 and 8760 is 15338760.
2. What are the Factors of 8755?
Answer: Factors of 8755 are 1, 5, 17, 85, 103, 515, 1751, 8755. There are 8 integers that are factors of 8755. The greatest factor of 8755 is 8755.
3. What are the Factors of 8760?
Answer: Factors of 8760 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 73, 120, 146, 219, 292, 365, 438, 584, 730, 876, 1095, 1460, 1752, 2190, 2920, 4380, 8760. There are 32 integers that are factors of 8760. The greatest factor of 8760 is 8760.
4. How to Find the LCM of 8755 and 8760?
Answer:
Least Common Multiple of 8755 and 8760 = 15338760
Step 1: Find the prime factorization of 8755
8755 = 5 x 17 x 103
Step 2: Find the prime factorization of 8760
8760 = 2 x 2 x 2 x 3 x 5 x 73
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 15338760 = 2 x 2 x 2 x 3 x 5 x 17 x 73 x 103
Step 4: Therefore, the least common multiple of 8755 and 8760 is 15338760.