Least Common Multiple (LCM) of 14 and 157
The least common multiple (LCM) of 14 and 157 is 2198.
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 14 and 157?
First, calculate the GCD of 14 and 157 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 14 ÷ 157 = 0 remainder 14 |
| 2 | 157 ÷ 14 = 11 remainder 3 |
| 3 | 14 ÷ 3 = 4 remainder 2 |
| 4 | 3 ÷ 2 = 1 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 100 and 151 | 15100 |
| 152 and 120 | 2280 |
| 128 and 92 | 2944 |
| 115 and 116 | 13340 |
| 162 and 114 | 3078 |