Least Common Multiple (LCM) of 168 and 178
The least common multiple (LCM) of 168 and 178 is 14952.
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 168 and 178?
First, calculate the GCD of 168 and 178 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 168 ÷ 178 = 0 remainder 168 |
| 2 | 178 ÷ 168 = 1 remainder 10 |
| 3 | 168 ÷ 10 = 16 remainder 8 |
| 4 | 10 ÷ 8 = 1 remainder 2 |
| 5 | 8 ÷ 2 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 120 and 97 | 11640 |
| 91 and 123 | 11193 |
| 49 and 160 | 7840 |
| 23 and 43 | 989 |
| 63 and 151 | 9513 |