Least Common Multiple (LCM) of 83 and 152
The least common multiple (LCM) of 83 and 152 is 12616.
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 152?
First, calculate the GCD of 83 and 152 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 83 ÷ 152 = 0 remainder 83 |
| 2 | 152 ÷ 83 = 1 remainder 69 |
| 3 | 83 ÷ 69 = 1 remainder 14 |
| 4 | 69 ÷ 14 = 4 remainder 13 |
| 5 | 14 ÷ 13 = 1 remainder 1 |
| 6 | 13 ÷ 1 = 13 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 132 and 85 | 11220 |
| 79 and 185 | 14615 |
| 165 and 112 | 18480 |
| 89 and 21 | 1869 |
| 134 and 27 | 3618 |