Least Common Multiple (LCM) of 103 and 156
The least common multiple (LCM) of 103 and 156 is 16068.
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 103 and 156?
First, calculate the GCD of 103 and 156 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 103 ÷ 156 = 0 remainder 103 |
| 2 | 156 ÷ 103 = 1 remainder 53 |
| 3 | 103 ÷ 53 = 1 remainder 50 |
| 4 | 53 ÷ 50 = 1 remainder 3 |
| 5 | 50 ÷ 3 = 16 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 144 and 140 | 5040 |
| 18 and 133 | 2394 |
| 65 and 142 | 9230 |
| 115 and 121 | 13915 |
| 72 and 148 | 2664 |