Least Common Multiple (LCM) of 179 and 68
The least common multiple (LCM) of 179 and 68 is 12172.
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 68?
First, calculate the GCD of 179 and 68 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 179 ÷ 68 = 2 remainder 43 |
| 2 | 68 ÷ 43 = 1 remainder 25 |
| 3 | 43 ÷ 25 = 1 remainder 18 |
| 4 | 25 ÷ 18 = 1 remainder 7 |
| 5 | 18 ÷ 7 = 2 remainder 4 |
| 6 | 7 ÷ 4 = 1 remainder 3 |
| 7 | 4 ÷ 3 = 1 remainder 1 |
| 8 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 29 and 121 | 3509 |
| 120 and 105 | 840 |
| 15 and 101 | 1515 |
| 119 and 83 | 9877 |
| 116 and 21 | 2436 |