Least Common Multiple (LCM) of 56 and 101
The least common multiple (LCM) of 56 and 101 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 56 and 101?
First, calculate the GCD of 56 and 101 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 56 ÷ 101 = 0 remainder 56 |
| 2 | 101 ÷ 56 = 1 remainder 45 |
| 3 | 56 ÷ 45 = 1 remainder 11 |
| 4 | 45 ÷ 11 = 4 remainder 1 |
| 5 | 11 ÷ 1 = 11 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 113 and 45 | 5085 |
| 196 and 198 | 19404 |
| 102 and 176 | 8976 |
| 170 and 131 | 22270 |
| 129 and 144 | 6192 |