Least Common Multiple (LCM) of 142 and 117
The least common multiple (LCM) of 142 and 117 is 16614.
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 142 and 117?
First, calculate the GCD of 142 and 117 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 142 ÷ 117 = 1 remainder 25 |
| 2 | 117 ÷ 25 = 4 remainder 17 |
| 3 | 25 ÷ 17 = 1 remainder 8 |
| 4 | 17 ÷ 8 = 2 remainder 1 |
| 5 | 8 ÷ 1 = 8 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 30 and 171 | 1710 |
| 133 and 45 | 5985 |
| 80 and 26 | 1040 |
| 172 and 42 | 3612 |
| 139 and 87 | 12093 |