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: ${P}_1+{P}_2+{P}_3$
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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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Question : If K1 and K2 are two distinct prime numbers, then what is the product of the highest common factor and the least common multiple of K1 and K2?
Option 1: $1$
Option 2: $\frac{K1}{K2}$
Option 3: $K1 + K2$
Option 4: $K1 × K2$
Question : If A, B and C are three distinct prime numbers, then what is the highest common factor of A, B and C?
Option 1: 7
Option 2: 0
Option 3: 5
Option 4: 1
Question : If A1 and A2 are two distinct prime numbers, then what is the highest common factor of A1 and A2?
Option 1: 3
Option 2: 1
Option 4: 2
Question : $P_1$ and $P_2$ can do a piece of work together in 14 days, $P_2$ and $P_3$ can do the same work together in 21 days, while $P_3$ and $P_1$ can do it together in 42 days. How much work can all the 3 together do in 12 days?
Option 1: $\frac{5}{6}$
Option 2: $\frac{5}{7}$
Option 3: $\frac{6}{7}$
Option 4: $\frac{3}{7}$
Question : The product of two co-prime numbers is 483. Find the Least Common Multiple of both numbers.
Option 1: 483
Option 2: 21
Option 3: 1
Option 4: 23
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