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Two positive numbers $m$ and $n$ are both divisible by $3$ , $5$ , $15$ , $25$ and $75$ . What is the hcf of $M$ and $N$

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Least common multiple of three or four numbers

Full solution

Q. Two positive numbers

m

and

n

are both divisible by

3

,

5

,

15

,

25

and

75

. What is the hcf of

M

and

N

Identify Common Divisors: Since $m$ and $n$ are both divisible by $3$ , $5$ , $15$ , $25$ , and $75$ , we need to find the highest common factor among these divisors.
Observe $75$ as Common Multiple: The divisors given are $3$ , $5$ , $15$ , $25$ , and $75$ . We can observe that $75$ is divisible by all the other divisors ( $3$ , $5$ , $15$ , and $25$ ). This means that $75$ is a common multiple of all the other divisors.
Confirm $75$ as Common Factor: If $75$ is a common multiple and both $m$ and $n$ are divisible by $75$ , then $75$ is also a common factor of $m$ and $n$ .
Determine Highest Common Factor: Since we are looking for the highest common factor and $75$ is the largest divisor given, it is the highest common factor of $m$ and $n$ .

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