Least Common Multiple (LCM) of 148 and 83
The least common multiple (LCM) of 148 and 83 is 12284.
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 83?
First, calculate the GCD of 148 and 83 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 148 ÷ 83 = 1 remainder 65 |
| 2 | 83 ÷ 65 = 1 remainder 18 |
| 3 | 65 ÷ 18 = 3 remainder 11 |
| 4 | 18 ÷ 11 = 1 remainder 7 |
| 5 | 11 ÷ 7 = 1 remainder 4 |
| 6 | 7 ÷ 4 = 1 remainder 3 |
| 7 | 4 ÷ 3 = 1 remainder 1 |
| 8 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 100 and 55 | 1100 |
| 121 and 84 | 10164 |
| 194 and 17 | 3298 |
| 169 and 125 | 21125 |
| 120 and 40 | 120 |