Least Common Multiple (LCM) of 68 and 178
The least common multiple (LCM) of 68 and 178 is 6052.
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 178?
First, calculate the GCD of 68 and 178 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 68 ÷ 178 = 0 remainder 68 |
| 2 | 178 ÷ 68 = 2 remainder 42 |
| 3 | 68 ÷ 42 = 1 remainder 26 |
| 4 | 42 ÷ 26 = 1 remainder 16 |
| 5 | 26 ÷ 16 = 1 remainder 10 |
| 6 | 16 ÷ 10 = 1 remainder 6 |
| 7 | 10 ÷ 6 = 1 remainder 4 |
| 8 | 6 ÷ 4 = 1 remainder 2 |
| 9 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 120 and 94 | 5640 |
| 116 and 164 | 4756 |
| 82 and 172 | 7052 |
| 176 and 59 | 10384 |
| 45 and 28 | 1260 |