Least Common Multiple (LCM) of 42 and 122
The least common multiple (LCM) of 42 and 122 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 122?
First, calculate the GCD of 42 and 122 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 42 ÷ 122 = 0 remainder 42 |
| 2 | 122 ÷ 42 = 2 remainder 38 |
| 3 | 42 ÷ 38 = 1 remainder 4 |
| 4 | 38 ÷ 4 = 9 remainder 2 |
| 5 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 161 and 93 | 14973 |
| 104 and 92 | 2392 |
| 43 and 73 | 3139 |
| 166 and 67 | 11122 |
| 185 and 180 | 6660 |