Least Common Multiple (LCM) of 101 and 64
The least common multiple (LCM) of 101 and 64 is 6464.
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 101 and 64?
First, calculate the GCD of 101 and 64 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 101 ÷ 64 = 1 remainder 37 |
| 2 | 64 ÷ 37 = 1 remainder 27 |
| 3 | 37 ÷ 27 = 1 remainder 10 |
| 4 | 27 ÷ 10 = 2 remainder 7 |
| 5 | 10 ÷ 7 = 1 remainder 3 |
| 6 | 7 ÷ 3 = 2 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 86 and 37 | 3182 |
| 31 and 74 | 2294 |
| 101 and 126 | 12726 |
| 185 and 93 | 17205 |
| 36 and 107 | 3852 |