Least Common Multiple (LCM) of 54 and 152
The least common multiple (LCM) of 54 and 152 is 4104.
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 54 and 152?
First, calculate the GCD of 54 and 152 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 54 ÷ 152 = 0 remainder 54 |
| 2 | 152 ÷ 54 = 2 remainder 44 |
| 3 | 54 ÷ 44 = 1 remainder 10 |
| 4 | 44 ÷ 10 = 4 remainder 4 |
| 5 | 10 ÷ 4 = 2 remainder 2 |
| 6 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 119 and 198 | 23562 |
| 35 and 59 | 2065 |
| 174 and 31 | 5394 |
| 170 and 30 | 510 |
| 47 and 166 | 7802 |