Least Common Multiple (LCM) of 49 and 178
The least common multiple (LCM) of 49 and 178 is 8722.
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 49 and 178?
First, calculate the GCD of 49 and 178 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 49 ÷ 178 = 0 remainder 49 |
| 2 | 178 ÷ 49 = 3 remainder 31 |
| 3 | 49 ÷ 31 = 1 remainder 18 |
| 4 | 31 ÷ 18 = 1 remainder 13 |
| 5 | 18 ÷ 13 = 1 remainder 5 |
| 6 | 13 ÷ 5 = 2 remainder 3 |
| 7 | 5 ÷ 3 = 1 remainder 2 |
| 8 | 3 ÷ 2 = 1 remainder 1 |
| 9 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 34 and 194 | 3298 |
| 27 and 16 | 432 |
| 58 and 182 | 5278 |
| 25 and 113 | 2825 |
| 38 and 200 | 3800 |