Least Common Multiple (LCM) of 154 and 178
The least common multiple (LCM) of 154 and 178 is 13706.
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 154 and 178?
First, calculate the GCD of 154 and 178 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 154 ÷ 178 = 0 remainder 154 |
| 2 | 178 ÷ 154 = 1 remainder 24 |
| 3 | 154 ÷ 24 = 6 remainder 10 |
| 4 | 24 ÷ 10 = 2 remainder 4 |
| 5 | 10 ÷ 4 = 2 remainder 2 |
| 6 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 71 and 81 | 5751 |
| 104 and 55 | 5720 |
| 134 and 155 | 20770 |
| 33 and 142 | 4686 |
| 70 and 38 | 1330 |