Least Common Multiple (LCM) of 100 and 101
The least common multiple (LCM) of 100 and 101 is 10100.
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 101?
First, calculate the GCD of 100 and 101 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 100 ÷ 101 = 0 remainder 100 |
| 2 | 101 ÷ 100 = 1 remainder 1 |
| 3 | 100 ÷ 1 = 100 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 35 and 100 | 700 |
| 192 and 136 | 3264 |
| 183 and 115 | 21045 |
| 30 and 121 | 3630 |
| 18 and 192 | 576 |