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 |
|---|---|
| 11 and 132 | 132 |
| 178 and 136 | 12104 |
| 39 and 168 | 2184 |
| 92 and 194 | 8924 |
| 162 and 124 | 10044 |