Least Common Multiple (LCM) of 179 and 193
The least common multiple (LCM) of 179 and 193 is 34547.
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 179 and 193?
First, calculate the GCD of 179 and 193 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 179 ÷ 193 = 0 remainder 179 |
| 2 | 193 ÷ 179 = 1 remainder 14 |
| 3 | 179 ÷ 14 = 12 remainder 11 |
| 4 | 14 ÷ 11 = 1 remainder 3 |
| 5 | 11 ÷ 3 = 3 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 160 and 15 | 480 |
| 32 and 52 | 416 |
| 12 and 106 | 636 |
| 90 and 79 | 7110 |
| 22 and 192 | 2112 |