Least Common Multiple (LCM) of 106 and 179
The least common multiple (LCM) of 106 and 179 is 18974.
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 106 and 179?
First, calculate the GCD of 106 and 179 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 106 ÷ 179 = 0 remainder 106 |
| 2 | 179 ÷ 106 = 1 remainder 73 |
| 3 | 106 ÷ 73 = 1 remainder 33 |
| 4 | 73 ÷ 33 = 2 remainder 7 |
| 5 | 33 ÷ 7 = 4 remainder 5 |
| 6 | 7 ÷ 5 = 1 remainder 2 |
| 7 | 5 ÷ 2 = 2 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 113 and 31 | 3503 |
| 46 and 118 | 2714 |
| 176 and 62 | 5456 |
| 54 and 174 | 1566 |
| 106 and 44 | 2332 |