Question

three alarm clock ring at intervals of 4 12 and 20 minutes respectively if they start ringing together after how much time will they next ring together​

Answer 1

$\large{\underline{\rm{\green{\bf{Given:-}}}}}$

Clock will ring at an interval of 4, 12, 20 minutes

$\large{\underline{\rm{\green{\bf{To \: Find:-}}}}}$

When will the clocks ring together next.

$\large{\underline{\rm{\green{\bf{Analysis:-}}}}}$

Find the LCM of 4, 12, 20 in order to get the next time when will the clock ring.

$\large{\underline{\rm{\green{\bf{Solution:-}}}}}$

Given that, the clock will ring at an interval of 4, 12, 20

According to the analysis given, to find the next time we have to get the LCM of these three numbers.

Then, the LCM of 4, 12, 20

$\implies \sf LCM=4 \times 1 \times 3 \times 5$

$\implies \sf LCM=60$

Least common multiple is 60

Therefore, the clock will ring again together after 60 minutes.

$\large{\underline{\rm{\green{\bf{To \: Note:-}}}}}$

One way to find the least common multiple of two numbers is to first list the prime factors of each number. Then multiply each factor the greatest number of times it occurs in either number.

A multiple is a number you get when you multiply a number by a whole number (greater than 0) is called LCM

Answer 2

Answer:

Thus, we found the LCM of 4, 12 and 20 to be 2×2×3×5=60 . Hence, the three clocks will ring together after 60 minutes or 1 hour. Note: You may take HCF instead of LCM.

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