Least Common Multiple (LCM) of 61 and 101
The least common multiple (LCM) of 61 and 101 is 6161.
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 61 and 101?
First, calculate the GCD of 61 and 101 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 61 ÷ 101 = 0 remainder 61 |
| 2 | 101 ÷ 61 = 1 remainder 40 |
| 3 | 61 ÷ 40 = 1 remainder 21 |
| 4 | 40 ÷ 21 = 1 remainder 19 |
| 5 | 21 ÷ 19 = 1 remainder 2 |
| 6 | 19 ÷ 2 = 9 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 20 and 173 | 3460 |
| 24 and 33 | 264 |
| 65 and 180 | 2340 |
| 16 and 199 | 3184 |
| 108 and 106 | 5724 |