Least Common Multiple (LCM) of 110 and 156
The least common multiple (LCM) of 110 and 156 is 8580.
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 156?
First, calculate the GCD of 110 and 156 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 110 ÷ 156 = 0 remainder 110 |
| 2 | 156 ÷ 110 = 1 remainder 46 |
| 3 | 110 ÷ 46 = 2 remainder 18 |
| 4 | 46 ÷ 18 = 2 remainder 10 |
| 5 | 18 ÷ 10 = 1 remainder 8 |
| 6 | 10 ÷ 8 = 1 remainder 2 |
| 7 | 8 ÷ 2 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 144 and 21 | 1008 |
| 107 and 50 | 5350 |
| 151 and 189 | 28539 |
| 93 and 27 | 837 |
| 35 and 141 | 4935 |