Least Common Multiple (LCM) of 61 and 102
The least common multiple (LCM) of 61 and 102 is 6222.
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 102?
First, calculate the GCD of 61 and 102 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 61 ÷ 102 = 0 remainder 61 |
| 2 | 102 ÷ 61 = 1 remainder 41 |
| 3 | 61 ÷ 41 = 1 remainder 20 |
| 4 | 41 ÷ 20 = 2 remainder 1 |
| 5 | 20 ÷ 1 = 20 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 165 and 76 | 12540 |
| 156 and 40 | 1560 |
| 119 and 35 | 595 |
| 47 and 140 | 6580 |
| 110 and 169 | 18590 |