Least Common Multiple (LCM) of 72 and 178
The least common multiple (LCM) of 72 and 178 is 6408.
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 72 and 178?
First, calculate the GCD of 72 and 178 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 72 ÷ 178 = 0 remainder 72 |
| 2 | 178 ÷ 72 = 2 remainder 34 |
| 3 | 72 ÷ 34 = 2 remainder 4 |
| 4 | 34 ÷ 4 = 8 remainder 2 |
| 5 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 117 and 26 | 234 |
| 139 and 80 | 11120 |
| 48 and 133 | 6384 |
| 77 and 47 | 3619 |
| 95 and 142 | 13490 |