Least Common Multiple (LCM) of 153 and 84
The least common multiple (LCM) of 153 and 84 is 4284.
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 84?
First, calculate the GCD of 153 and 84 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 153 ÷ 84 = 1 remainder 69 |
| 2 | 84 ÷ 69 = 1 remainder 15 |
| 3 | 69 ÷ 15 = 4 remainder 9 |
| 4 | 15 ÷ 9 = 1 remainder 6 |
| 5 | 9 ÷ 6 = 1 remainder 3 |
| 6 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 29 and 83 | 2407 |
| 18 and 103 | 1854 |
| 30 and 126 | 630 |
| 13 and 46 | 598 |
| 132 and 193 | 25476 |