Least Common Multiple (LCM) of 179 and 69
The least common multiple (LCM) of 179 and 69 is 12351.
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 69?
First, calculate the GCD of 179 and 69 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 179 ÷ 69 = 2 remainder 41 |
| 2 | 69 ÷ 41 = 1 remainder 28 |
| 3 | 41 ÷ 28 = 1 remainder 13 |
| 4 | 28 ÷ 13 = 2 remainder 2 |
| 5 | 13 ÷ 2 = 6 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 85 and 34 | 170 |
| 158 and 73 | 11534 |
| 125 and 101 | 12625 |
| 109 and 194 | 21146 |
| 30 and 59 | 1770 |