Least Common Multiple (LCM) of 157 and 191
The least common multiple (LCM) of 157 and 191 is 29987.
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 191?
First, calculate the GCD of 157 and 191 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 157 ÷ 191 = 0 remainder 157 |
| 2 | 191 ÷ 157 = 1 remainder 34 |
| 3 | 157 ÷ 34 = 4 remainder 21 |
| 4 | 34 ÷ 21 = 1 remainder 13 |
| 5 | 21 ÷ 13 = 1 remainder 8 |
| 6 | 13 ÷ 8 = 1 remainder 5 |
| 7 | 8 ÷ 5 = 1 remainder 3 |
| 8 | 5 ÷ 3 = 1 remainder 2 |
| 9 | 3 ÷ 2 = 1 remainder 1 |
| 10 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 162 and 79 | 12798 |
| 27 and 61 | 1647 |
| 14 and 11 | 154 |
| 120 and 47 | 5640 |
| 46 and 67 | 3082 |