Least Common Multiple (LCM) of 42 and 141
The least common multiple (LCM) of 42 and 141 is 1974.
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 141?
First, calculate the GCD of 42 and 141 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 42 ÷ 141 = 0 remainder 42 |
| 2 | 141 ÷ 42 = 3 remainder 15 |
| 3 | 42 ÷ 15 = 2 remainder 12 |
| 4 | 15 ÷ 12 = 1 remainder 3 |
| 5 | 12 ÷ 3 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 42 and 10 | 210 |
| 160 and 24 | 480 |
| 134 and 51 | 6834 |
| 52 and 162 | 4212 |
| 41 and 21 | 861 |