Least Common Multiple (LCM) of 61 and 146
The least common multiple (LCM) of 61 and 146 is 8906.
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 146?
First, calculate the GCD of 61 and 146 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 61 ÷ 146 = 0 remainder 61 |
| 2 | 146 ÷ 61 = 2 remainder 24 |
| 3 | 61 ÷ 24 = 2 remainder 13 |
| 4 | 24 ÷ 13 = 1 remainder 11 |
| 5 | 13 ÷ 11 = 1 remainder 2 |
| 6 | 11 ÷ 2 = 5 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 189 and 135 | 945 |
| 132 and 165 | 660 |
| 174 and 200 | 17400 |
| 75 and 195 | 975 |
| 181 and 98 | 17738 |