Least Common Multiple (LCM) of 153 and 103
The least common multiple (LCM) of 153 and 103 is 15759.
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 153 and 103?
First, calculate the GCD of 153 and 103 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 153 ÷ 103 = 1 remainder 50 |
| 2 | 103 ÷ 50 = 2 remainder 3 |
| 3 | 50 ÷ 3 = 16 remainder 2 |
| 4 | 3 ÷ 2 = 1 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 107 and 143 | 15301 |
| 144 and 16 | 144 |
| 20 and 110 | 220 |
| 83 and 147 | 12201 |
| 119 and 126 | 2142 |