Least Common Multiple (LCM) of 84 and 153
The least common multiple (LCM) of 84 and 153 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 84 and 153?
First, calculate the GCD of 84 and 153 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 84 ÷ 153 = 0 remainder 84 |
| 2 | 153 ÷ 84 = 1 remainder 69 |
| 3 | 84 ÷ 69 = 1 remainder 15 |
| 4 | 69 ÷ 15 = 4 remainder 9 |
| 5 | 15 ÷ 9 = 1 remainder 6 |
| 6 | 9 ÷ 6 = 1 remainder 3 |
| 7 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 180 and 182 | 16380 |
| 38 and 103 | 3914 |
| 64 and 63 | 4032 |
| 164 and 32 | 1312 |
| 124 and 42 | 2604 |