Least Common Multiple (LCM) of 82 and 151
The least common multiple (LCM) of 82 and 151 is 12382.
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 151?
First, calculate the GCD of 82 and 151 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 82 ÷ 151 = 0 remainder 82 |
| 2 | 151 ÷ 82 = 1 remainder 69 |
| 3 | 82 ÷ 69 = 1 remainder 13 |
| 4 | 69 ÷ 13 = 5 remainder 4 |
| 5 | 13 ÷ 4 = 3 remainder 1 |
| 6 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 36 and 105 | 1260 |
| 158 and 160 | 12640 |
| 141 and 61 | 8601 |
| 28 and 33 | 924 |
| 90 and 149 | 13410 |