Least Common Multiple (LCM) of 148 and 117
The least common multiple (LCM) of 148 and 117 is 17316.
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 148 and 117?
First, calculate the GCD of 148 and 117 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 148 ÷ 117 = 1 remainder 31 |
| 2 | 117 ÷ 31 = 3 remainder 24 |
| 3 | 31 ÷ 24 = 1 remainder 7 |
| 4 | 24 ÷ 7 = 3 remainder 3 |
| 5 | 7 ÷ 3 = 2 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 188 and 112 | 5264 |
| 135 and 24 | 1080 |
| 34 and 104 | 1768 |
| 118 and 72 | 4248 |
| 123 and 113 | 13899 |