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 |
|---|---|
| 171 and 43 | 7353 |
| 116 and 158 | 9164 |
| 155 and 149 | 23095 |
| 174 and 161 | 28014 |
| 11 and 108 | 1188 |