Least Common Multiple (LCM) of 12 and 117
The least common multiple (LCM) of 12 and 117 is 468.
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 12 and 117?
First, calculate the GCD of 12 and 117 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 12 ÷ 117 = 0 remainder 12 |
| 2 | 117 ÷ 12 = 9 remainder 9 |
| 3 | 12 ÷ 9 = 1 remainder 3 |
| 4 | 9 ÷ 3 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 44 and 84 | 924 |
| 35 and 97 | 3395 |
| 102 and 159 | 5406 |
| 86 and 141 | 12126 |
| 155 and 125 | 3875 |