Least Common Multiple (LCM) of 53 and 189
The least common multiple (LCM) of 53 and 189 is 10017.
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 53 and 189?
First, calculate the GCD of 53 and 189 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 53 ÷ 189 = 0 remainder 53 |
| 2 | 189 ÷ 53 = 3 remainder 30 |
| 3 | 53 ÷ 30 = 1 remainder 23 |
| 4 | 30 ÷ 23 = 1 remainder 7 |
| 5 | 23 ÷ 7 = 3 remainder 2 |
| 6 | 7 ÷ 2 = 3 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 154 and 112 | 1232 |
| 152 and 73 | 11096 |
| 162 and 123 | 6642 |
| 14 and 195 | 2730 |
| 104 and 34 | 1768 |