Least Common Multiple (LCM) of 117 and 152
The least common multiple (LCM) of 117 and 152 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 117 and 152?
First, calculate the GCD of 117 and 152 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 117 ÷ 152 = 0 remainder 117 |
| 2 | 152 ÷ 117 = 1 remainder 35 |
| 3 | 117 ÷ 35 = 3 remainder 12 |
| 4 | 35 ÷ 12 = 2 remainder 11 |
| 5 | 12 ÷ 11 = 1 remainder 1 |
| 6 | 11 ÷ 1 = 11 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 53 and 29 | 1537 |
| 81 and 115 | 9315 |
| 109 and 35 | 3815 |
| 180 and 171 | 3420 |
| 141 and 166 | 23406 |