Least Common Multiple (LCM) of 100 and 40
The least common multiple (LCM) of 100 and 40 is 200.
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 40?
First, calculate the GCD of 100 and 40 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 100 ÷ 40 = 2 remainder 20 |
| 2 | 40 ÷ 20 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 140 and 144 | 5040 |
| 192 and 186 | 5952 |
| 60 and 69 | 1380 |
| 45 and 160 | 1440 |
| 175 and 199 | 34825 |