Least Common Multiple (LCM) of 109 and 148
The least common multiple (LCM) of 109 and 148 is 16132.
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 109 and 148?
First, calculate the GCD of 109 and 148 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 109 ÷ 148 = 0 remainder 109 |
| 2 | 148 ÷ 109 = 1 remainder 39 |
| 3 | 109 ÷ 39 = 2 remainder 31 |
| 4 | 39 ÷ 31 = 1 remainder 8 |
| 5 | 31 ÷ 8 = 3 remainder 7 |
| 6 | 8 ÷ 7 = 1 remainder 1 |
| 7 | 7 ÷ 1 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 76 and 186 | 7068 |
| 18 and 130 | 1170 |
| 168 and 37 | 6216 |
| 51 and 161 | 8211 |
| 180 and 89 | 16020 |