Least Common Multiple (LCM) of 42 and 61
The least common multiple (LCM) of 42 and 61 is 2562.
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 42 and 61?
First, calculate the GCD of 42 and 61 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 42 ÷ 61 = 0 remainder 42 |
| 2 | 61 ÷ 42 = 1 remainder 19 |
| 3 | 42 ÷ 19 = 2 remainder 4 |
| 4 | 19 ÷ 4 = 4 remainder 3 |
| 5 | 4 ÷ 3 = 1 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 17 and 104 | 1768 |
| 199 and 70 | 13930 |
| 159 and 89 | 14151 |
| 160 and 164 | 6560 |
| 67 and 173 | 11591 |