Least Common Multiple (LCM) of 82 and 153
The least common multiple (LCM) of 82 and 153 is 12546.
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 82 and 153?
First, calculate the GCD of 82 and 153 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 82 ÷ 153 = 0 remainder 82 |
| 2 | 153 ÷ 82 = 1 remainder 71 |
| 3 | 82 ÷ 71 = 1 remainder 11 |
| 4 | 71 ÷ 11 = 6 remainder 5 |
| 5 | 11 ÷ 5 = 2 remainder 1 |
| 6 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 15 and 199 | 2985 |
| 112 and 192 | 1344 |
| 39 and 169 | 507 |
| 106 and 47 | 4982 |
| 20 and 143 | 2860 |