Least Common Multiple (LCM) of 102 and 156
The least common multiple (LCM) of 102 and 156 is 2652.
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 102 and 156?
First, calculate the GCD of 102 and 156 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 102 ÷ 156 = 0 remainder 102 |
| 2 | 156 ÷ 102 = 1 remainder 54 |
| 3 | 102 ÷ 54 = 1 remainder 48 |
| 4 | 54 ÷ 48 = 1 remainder 6 |
| 5 | 48 ÷ 6 = 8 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 120 and 129 | 5160 |
| 130 and 16 | 1040 |
| 21 and 99 | 693 |
| 184 and 199 | 36616 |
| 74 and 75 | 5550 |