Least Common Multiple (LCM) of 100 and 118
The least common multiple (LCM) of 100 and 118 is 5900.
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 118?
First, calculate the GCD of 100 and 118 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 100 ÷ 118 = 0 remainder 100 |
| 2 | 118 ÷ 100 = 1 remainder 18 |
| 3 | 100 ÷ 18 = 5 remainder 10 |
| 4 | 18 ÷ 10 = 1 remainder 8 |
| 5 | 10 ÷ 8 = 1 remainder 2 |
| 6 | 8 ÷ 2 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 104 and 126 | 6552 |
| 25 and 110 | 550 |
| 198 and 99 | 198 |
| 131 and 76 | 9956 |
| 167 and 50 | 8350 |