Least Common Multiple (LCM) of 110 and 153
The least common multiple (LCM) of 110 and 153 is 16830.
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 153?
First, calculate the GCD of 110 and 153 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 110 ÷ 153 = 0 remainder 110 |
| 2 | 153 ÷ 110 = 1 remainder 43 |
| 3 | 110 ÷ 43 = 2 remainder 24 |
| 4 | 43 ÷ 24 = 1 remainder 19 |
| 5 | 24 ÷ 19 = 1 remainder 5 |
| 6 | 19 ÷ 5 = 3 remainder 4 |
| 7 | 5 ÷ 4 = 1 remainder 1 |
| 8 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 190 and 132 | 12540 |
| 157 and 165 | 25905 |
| 35 and 15 | 105 |
| 61 and 132 | 8052 |
| 180 and 119 | 21420 |