Least Common Multiple (LCM) of 101 and 56
The least common multiple (LCM) of 101 and 56 is 5656.
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 56?
First, calculate the GCD of 101 and 56 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 101 ÷ 56 = 1 remainder 45 |
| 2 | 56 ÷ 45 = 1 remainder 11 |
| 3 | 45 ÷ 11 = 4 remainder 1 |
| 4 | 11 ÷ 1 = 11 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 154 and 72 | 5544 |
| 71 and 32 | 2272 |
| 108 and 178 | 9612 |
| 120 and 61 | 7320 |
| 101 and 130 | 13130 |