Question : If ${P}_1, {P}_2$, and ${P}_3$ are three distinct prime numbers, then what is the least common multiple of ${P}_1, {P}_2$, and ${P}_3$ ?
Option 1: $P_1$
Option 2: $P_1 \times P_2 \times P_3$
Option 3: $P_2 \times P_3$
Option 4: ${P}_1+{P}_2+{P}_3$
Correct Answer: $P_1 \times P_2 \times P_3$
Solution :
The least common multiple (LCM) of three distinct prime numbers, P1, P2, and P3, is simply their product, $P_1 \times P_2 \times P_3$.
To see why, we can use the fact that the LCM of any set of numbers is the smallest positive integer that is divisible by all the numbers in the set. Since $P_1,P_2, P_3$ are prime numbers, their only positive divisors are 1 and themselves. Therefore, any positive integer that is divisible by all three primes must be a multiple of their product, $P_1 \times P_2 \times P_3$.
Since $P_1,P_2, P_3$ are distinct primes, their product is not divisible by any other prime number. Therefore, $P_1 \times P_2 \times P_3$ is the smallest positive integer divisible by all three primes; hence, it is their LCM.
Hence, the correct answer is $P_1 \times P_2 \times P_3$.
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