Number System

HCF & LCM

Easy

3 bells ring at intervals of 3hrs, 4hrs and 16hrs respectively. If they have rung together once today, what day in the future will they ring together next?

5 days hence

Tomorrow

3 days hence

Day after tomorrow

✅ Correct Option: 4

The bells will ring together again at the LCM (Least Common Multiple) of their intervals.

Prime factorization of each interval:

$3 = 3^1$

$4 = 2^2$

$16 = 2^4$

The LCM takes the highest power of each prime factor:

Highest power of $2 = 2^4 = 16$

Highest power of $3 = 3^1 = 3$

$\text{LCM} = 16 \times 3$

$\text{LCM} = 48$ hours

Converting to days:

$\dfrac{48 \text{ hours}}{24 \text{ hours/day}} = 2 \text{ days}$

The bells will ring together again in $2$ days from today.

BMSAT Kozhikode 2026

Integer multiples of 3 are arranged in increasing order, starting with 3, such that the difference between $k^{th}$ number in this list and $(k+1)^{th}$ is the LCM of 3 and $k$ . Calculate the sum of the first 5 numbers.

BMSAT Kozhikode 2026

If the HCF of two natural numbers is 12 and the product of the numbers is 2028, how many such pairs exist?

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There are 56 runners and 40 musicians in a school. These students are arranged into groups for a performance, so that each group consists of only runners or musicians, and every group contains an equal number of students. Find the minimum number of groups in which all the students can be accommodated?

3 bells ring at intervals of 3hrs, 4hrs and 16hrs respectively. If they have rung together once today, what day in the future will they ring together next?

Solution

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