Least Common Multiple (LCM) of 100 and 113
The least common multiple (LCM) of 100 and 113 is 11300.
What is the Least Common Multiple (LCM)?
The LCM of two integers is the smallest positive integer that is divisible by both numbers. It is often used to find common denominators and solve problems involving periodic events.
Formula for LCM
The LCM of two numbers can be calculated using their GCD:
LCM(a, b) = |a × b| ÷ GCD(a, b)
How to Calculate the LCM of 100 and 113?
First, calculate the GCD of 100 and 113 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 100 ÷ 113 = 0 remainder 100 |
| 2 | 113 ÷ 100 = 1 remainder 13 |
| 3 | 100 ÷ 13 = 7 remainder 9 |
| 4 | 13 ÷ 9 = 1 remainder 4 |
| 5 | 9 ÷ 4 = 2 remainder 1 |
| 6 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 113 and 87 | 9831 |
| 96 and 76 | 1824 |
| 64 and 63 | 4032 |
| 167 and 179 | 29893 |
| 34 and 141 | 4794 |