Least Common Multiple (LCM) of 68 and 179
The least common multiple (LCM) of 68 and 179 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 68 and 179?
First, calculate the GCD of 68 and 179 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 68 ÷ 179 = 0 remainder 68 |
| 2 | 179 ÷ 68 = 2 remainder 43 |
| 3 | 68 ÷ 43 = 1 remainder 25 |
| 4 | 43 ÷ 25 = 1 remainder 18 |
| 5 | 25 ÷ 18 = 1 remainder 7 |
| 6 | 18 ÷ 7 = 2 remainder 4 |
| 7 | 7 ÷ 4 = 1 remainder 3 |
| 8 | 4 ÷ 3 = 1 remainder 1 |
| 9 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 126 and 81 | 1134 |
| 17 and 108 | 1836 |
| 73 and 14 | 1022 |
| 179 and 126 | 22554 |
| 98 and 160 | 7840 |