Least Common Multiple (LCM) of 100 and 107
The least common multiple (LCM) of 100 and 107 is 10700.
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 107?
First, calculate the GCD of 100 and 107 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 100 ÷ 107 = 0 remainder 100 |
| 2 | 107 ÷ 100 = 1 remainder 7 |
| 3 | 100 ÷ 7 = 14 remainder 2 |
| 4 | 7 ÷ 2 = 3 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 101 and 165 | 16665 |
| 194 and 109 | 21146 |
| 139 and 195 | 27105 |
| 177 and 63 | 3717 |
| 92 and 51 | 4692 |