Least Common Multiple (LCM) of 83 and 153
The least common multiple (LCM) of 83 and 153 is 12699.
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 153?
First, calculate the GCD of 83 and 153 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 83 ÷ 153 = 0 remainder 83 |
| 2 | 153 ÷ 83 = 1 remainder 70 |
| 3 | 83 ÷ 70 = 1 remainder 13 |
| 4 | 70 ÷ 13 = 5 remainder 5 |
| 5 | 13 ÷ 5 = 2 remainder 3 |
| 6 | 5 ÷ 3 = 1 remainder 2 |
| 7 | 3 ÷ 2 = 1 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 170 and 123 | 20910 |
| 55 and 153 | 8415 |
| 114 and 71 | 8094 |
| 126 and 78 | 1638 |
| 175 and 117 | 20475 |