Least Common Multiple (LCM) of 117 and 148
The least common multiple (LCM) of 117 and 148 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 117 and 148?
First, calculate the GCD of 117 and 148 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 117 ÷ 148 = 0 remainder 117 |
| 2 | 148 ÷ 117 = 1 remainder 31 |
| 3 | 117 ÷ 31 = 3 remainder 24 |
| 4 | 31 ÷ 24 = 1 remainder 7 |
| 5 | 24 ÷ 7 = 3 remainder 3 |
| 6 | 7 ÷ 3 = 2 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 108 and 188 | 5076 |
| 189 and 131 | 24759 |
| 67 and 105 | 7035 |
| 82 and 97 | 7954 |
| 151 and 73 | 11023 |