Least Common Multiple (LCM) of 83 and 148
The least common multiple (LCM) of 83 and 148 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 83 and 148?
First, calculate the GCD of 83 and 148 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 83 ÷ 148 = 0 remainder 83 |
| 2 | 148 ÷ 83 = 1 remainder 65 |
| 3 | 83 ÷ 65 = 1 remainder 18 |
| 4 | 65 ÷ 18 = 3 remainder 11 |
| 5 | 18 ÷ 11 = 1 remainder 7 |
| 6 | 11 ÷ 7 = 1 remainder 4 |
| 7 | 7 ÷ 4 = 1 remainder 3 |
| 8 | 4 ÷ 3 = 1 remainder 1 |
| 9 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 96 and 65 | 6240 |
| 56 and 16 | 112 |
| 59 and 48 | 2832 |
| 120 and 45 | 360 |
| 162 and 88 | 7128 |