Least Common Multiple (LCM) of 100 and 102
The least common multiple (LCM) of 100 and 102 is 5100.
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 102?
First, calculate the GCD of 100 and 102 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 100 ÷ 102 = 0 remainder 100 |
| 2 | 102 ÷ 100 = 1 remainder 2 |
| 3 | 100 ÷ 2 = 50 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 129 and 10 | 1290 |
| 71 and 177 | 12567 |
| 108 and 177 | 6372 |
| 126 and 33 | 1386 |
| 160 and 85 | 2720 |