Least Common Multiple (LCM) of 110 and 152
The least common multiple (LCM) of 110 and 152 is 8360.
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 152?
First, calculate the GCD of 110 and 152 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 110 ÷ 152 = 0 remainder 110 |
| 2 | 152 ÷ 110 = 1 remainder 42 |
| 3 | 110 ÷ 42 = 2 remainder 26 |
| 4 | 42 ÷ 26 = 1 remainder 16 |
| 5 | 26 ÷ 16 = 1 remainder 10 |
| 6 | 16 ÷ 10 = 1 remainder 6 |
| 7 | 10 ÷ 6 = 1 remainder 4 |
| 8 | 6 ÷ 4 = 1 remainder 2 |
| 9 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 63 and 196 | 1764 |
| 90 and 44 | 1980 |
| 200 and 32 | 800 |
| 109 and 143 | 15587 |
| 149 and 142 | 21158 |