Least Common Multiple (LCM) of 61 and 145
The least common multiple (LCM) of 61 and 145 is 8845.
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 145?
First, calculate the GCD of 61 and 145 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 61 ÷ 145 = 0 remainder 61 |
| 2 | 145 ÷ 61 = 2 remainder 23 |
| 3 | 61 ÷ 23 = 2 remainder 15 |
| 4 | 23 ÷ 15 = 1 remainder 8 |
| 5 | 15 ÷ 8 = 1 remainder 7 |
| 6 | 8 ÷ 7 = 1 remainder 1 |
| 7 | 7 ÷ 1 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 200 and 78 | 7800 |
| 87 and 171 | 4959 |
| 75 and 170 | 2550 |
| 48 and 92 | 1104 |
| 135 and 36 | 540 |