Least Common Multiple (LCM) of 61 and 161
The least common multiple (LCM) of 61 and 161 is 9821.
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 161?
First, calculate the GCD of 61 and 161 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 61 ÷ 161 = 0 remainder 61 |
| 2 | 161 ÷ 61 = 2 remainder 39 |
| 3 | 61 ÷ 39 = 1 remainder 22 |
| 4 | 39 ÷ 22 = 1 remainder 17 |
| 5 | 22 ÷ 17 = 1 remainder 5 |
| 6 | 17 ÷ 5 = 3 remainder 2 |
| 7 | 5 ÷ 2 = 2 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 57 and 35 | 1995 |
| 93 and 123 | 3813 |
| 199 and 21 | 4179 |
| 22 and 148 | 1628 |
| 105 and 188 | 19740 |