Least Common Multiple (LCM) of 52 and 142
The least common multiple (LCM) of 52 and 142 is 3692.
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 52 and 142?
First, calculate the GCD of 52 and 142 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 52 ÷ 142 = 0 remainder 52 |
| 2 | 142 ÷ 52 = 2 remainder 38 |
| 3 | 52 ÷ 38 = 1 remainder 14 |
| 4 | 38 ÷ 14 = 2 remainder 10 |
| 5 | 14 ÷ 10 = 1 remainder 4 |
| 6 | 10 ÷ 4 = 2 remainder 2 |
| 7 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 64 and 132 | 2112 |
| 151 and 102 | 15402 |
| 145 and 122 | 17690 |
| 55 and 147 | 8085 |
| 54 and 136 | 3672 |