Least Common Multiple (LCM) of 157 and 46
The least common multiple (LCM) of 157 and 46 is 7222.
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 46?
First, calculate the GCD of 157 and 46 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 157 ÷ 46 = 3 remainder 19 |
| 2 | 46 ÷ 19 = 2 remainder 8 |
| 3 | 19 ÷ 8 = 2 remainder 3 |
| 4 | 8 ÷ 3 = 2 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 164 and 183 | 30012 |
| 192 and 150 | 4800 |
| 24 and 196 | 1176 |
| 77 and 79 | 6083 |
| 51 and 109 | 5559 |