Least Common Multiple (LCM) of 46 and 157
The least common multiple (LCM) of 46 and 157 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 46 and 157?
First, calculate the GCD of 46 and 157 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 46 ÷ 157 = 0 remainder 46 |
| 2 | 157 ÷ 46 = 3 remainder 19 |
| 3 | 46 ÷ 19 = 2 remainder 8 |
| 4 | 19 ÷ 8 = 2 remainder 3 |
| 5 | 8 ÷ 3 = 2 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 12 and 88 | 264 |
| 79 and 100 | 7900 |
| 17 and 36 | 612 |
| 33 and 76 | 2508 |
| 35 and 120 | 840 |