Least Common Multiple (LCM) of 100 and 64
The least common multiple (LCM) of 100 and 64 is 1600.
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 64?
First, calculate the GCD of 100 and 64 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 100 ÷ 64 = 1 remainder 36 |
| 2 | 64 ÷ 36 = 1 remainder 28 |
| 3 | 36 ÷ 28 = 1 remainder 8 |
| 4 | 28 ÷ 8 = 3 remainder 4 |
| 5 | 8 ÷ 4 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 122 and 67 | 8174 |
| 133 and 81 | 10773 |
| 10 and 22 | 110 |
| 23 and 83 | 1909 |
| 35 and 69 | 2415 |