Least Common Multiple (LCM) of 152 and 42
The least common multiple (LCM) of 152 and 42 is 3192.
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 152 and 42?
First, calculate the GCD of 152 and 42 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 152 ÷ 42 = 3 remainder 26 |
| 2 | 42 ÷ 26 = 1 remainder 16 |
| 3 | 26 ÷ 16 = 1 remainder 10 |
| 4 | 16 ÷ 10 = 1 remainder 6 |
| 5 | 10 ÷ 6 = 1 remainder 4 |
| 6 | 6 ÷ 4 = 1 remainder 2 |
| 7 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 63 and 31 | 1953 |
| 66 and 177 | 3894 |
| 71 and 33 | 2343 |
| 49 and 132 | 6468 |
| 61 and 170 | 10370 |