Least Common Multiple (LCM) of 110 and 157
The least common multiple (LCM) of 110 and 157 is 17270.
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 110 and 157?
First, calculate the GCD of 110 and 157 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 110 ÷ 157 = 0 remainder 110 |
| 2 | 157 ÷ 110 = 1 remainder 47 |
| 3 | 110 ÷ 47 = 2 remainder 16 |
| 4 | 47 ÷ 16 = 2 remainder 15 |
| 5 | 16 ÷ 15 = 1 remainder 1 |
| 6 | 15 ÷ 1 = 15 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 53 and 107 | 5671 |
| 127 and 164 | 20828 |
| 20 and 150 | 300 |
| 22 and 110 | 110 |
| 105 and 112 | 1680 |