Least Common Multiple (LCM) of 157 and 178
The least common multiple (LCM) of 157 and 178 is 27946.
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 157 and 178?
First, calculate the GCD of 157 and 178 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 157 ÷ 178 = 0 remainder 157 |
| 2 | 178 ÷ 157 = 1 remainder 21 |
| 3 | 157 ÷ 21 = 7 remainder 10 |
| 4 | 21 ÷ 10 = 2 remainder 1 |
| 5 | 10 ÷ 1 = 10 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 153 and 52 | 7956 |
| 187 and 35 | 6545 |
| 132 and 192 | 2112 |
| 100 and 56 | 1400 |
| 15 and 80 | 240 |