Least Common Multiple (LCM) of 83 and 135
The least common multiple (LCM) of 83 and 135 is 11205.
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 135?
First, calculate the GCD of 83 and 135 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 83 ÷ 135 = 0 remainder 83 |
| 2 | 135 ÷ 83 = 1 remainder 52 |
| 3 | 83 ÷ 52 = 1 remainder 31 |
| 4 | 52 ÷ 31 = 1 remainder 21 |
| 5 | 31 ÷ 21 = 1 remainder 10 |
| 6 | 21 ÷ 10 = 2 remainder 1 |
| 7 | 10 ÷ 1 = 10 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 152 and 21 | 3192 |
| 142 and 38 | 2698 |
| 175 and 184 | 32200 |
| 155 and 76 | 11780 |
| 67 and 128 | 8576 |