Least Common Multiple (LCM) of 100 and 65
The least common multiple (LCM) of 100 and 65 is 1300.
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 65?
First, calculate the GCD of 100 and 65 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 100 ÷ 65 = 1 remainder 35 |
| 2 | 65 ÷ 35 = 1 remainder 30 |
| 3 | 35 ÷ 30 = 1 remainder 5 |
| 4 | 30 ÷ 5 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 68 and 125 | 8500 |
| 185 and 35 | 1295 |
| 193 and 16 | 3088 |
| 137 and 112 | 15344 |
| 100 and 153 | 15300 |