Least Common Multiple (LCM) of 61 and 159
The least common multiple (LCM) of 61 and 159 is 9699.
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 159?
First, calculate the GCD of 61 and 159 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 61 ÷ 159 = 0 remainder 61 |
| 2 | 159 ÷ 61 = 2 remainder 37 |
| 3 | 61 ÷ 37 = 1 remainder 24 |
| 4 | 37 ÷ 24 = 1 remainder 13 |
| 5 | 24 ÷ 13 = 1 remainder 11 |
| 6 | 13 ÷ 11 = 1 remainder 2 |
| 7 | 11 ÷ 2 = 5 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 118 and 100 | 5900 |
| 75 and 109 | 8175 |
| 52 and 177 | 9204 |
| 137 and 12 | 1644 |
| 77 and 128 | 9856 |