Least Common Multiple (LCM) of 148 and 109
The least common multiple (LCM) of 148 and 109 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 148 and 109?
First, calculate the GCD of 148 and 109 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 148 ÷ 109 = 1 remainder 39 |
| 2 | 109 ÷ 39 = 2 remainder 31 |
| 3 | 39 ÷ 31 = 1 remainder 8 |
| 4 | 31 ÷ 8 = 3 remainder 7 |
| 5 | 8 ÷ 7 = 1 remainder 1 |
| 6 | 7 ÷ 1 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 41 and 42 | 1722 |
| 83 and 136 | 11288 |
| 35 and 175 | 175 |
| 120 and 132 | 1320 |
| 152 and 90 | 6840 |