Least Common Multiple (LCM) of 179 and 106
The least common multiple (LCM) of 179 and 106 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 179 and 106?
First, calculate the GCD of 179 and 106 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 179 ÷ 106 = 1 remainder 73 |
| 2 | 106 ÷ 73 = 1 remainder 33 |
| 3 | 73 ÷ 33 = 2 remainder 7 |
| 4 | 33 ÷ 7 = 4 remainder 5 |
| 5 | 7 ÷ 5 = 1 remainder 2 |
| 6 | 5 ÷ 2 = 2 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 35 and 70 | 70 |
| 53 and 74 | 3922 |
| 128 and 143 | 18304 |
| 50 and 67 | 3350 |
| 67 and 119 | 7973 |