Least Common Multiple (LCM) of 152 and 117
The least common multiple (LCM) of 152 and 117 is 17784.
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 152 and 117?
First, calculate the GCD of 152 and 117 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 152 ÷ 117 = 1 remainder 35 |
| 2 | 117 ÷ 35 = 3 remainder 12 |
| 3 | 35 ÷ 12 = 2 remainder 11 |
| 4 | 12 ÷ 11 = 1 remainder 1 |
| 5 | 11 ÷ 1 = 11 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 141 and 152 | 21432 |
| 121 and 19 | 2299 |
| 197 and 123 | 24231 |
| 31 and 76 | 2356 |
| 42 and 68 | 1428 |