Least Common Multiple (LCM) of 42 and 117
The least common multiple (LCM) of 42 and 117 is 1638.
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 117?
First, calculate the GCD of 42 and 117 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 42 ÷ 117 = 0 remainder 42 |
| 2 | 117 ÷ 42 = 2 remainder 33 |
| 3 | 42 ÷ 33 = 1 remainder 9 |
| 4 | 33 ÷ 9 = 3 remainder 6 |
| 5 | 9 ÷ 6 = 1 remainder 3 |
| 6 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 139 and 27 | 3753 |
| 32 and 126 | 2016 |
| 94 and 123 | 11562 |
| 87 and 93 | 2697 |
| 67 and 96 | 6432 |