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 |
|---|---|
| 131 and 192 | 25152 |
| 18 and 118 | 1062 |
| 136 and 24 | 408 |
| 151 and 159 | 24009 |
| 17 and 189 | 3213 |