Least Common Multiple (LCM) of 42 and 121
The least common multiple (LCM) of 42 and 121 is 5082.
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 121?
First, calculate the GCD of 42 and 121 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 42 ÷ 121 = 0 remainder 42 |
| 2 | 121 ÷ 42 = 2 remainder 37 |
| 3 | 42 ÷ 37 = 1 remainder 5 |
| 4 | 37 ÷ 5 = 7 remainder 2 |
| 5 | 5 ÷ 2 = 2 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 115 and 172 | 19780 |
| 10 and 95 | 190 |
| 182 and 44 | 4004 |
| 88 and 27 | 2376 |
| 173 and 45 | 7785 |