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Mathematics · 2023 · 3 marks
CBSE 2023 · Region 2 · Set 1 · Q26
Find by prime factorisation the LCM of the numbers $\displaystyle 18180$ and 7575. Also, find the HCF of the two numbers.Three bells ring at intervals of $\displaystyle 6$, $\displaystyle 12$ and $\displaystyle 18$ minutes. If all the three bells rang at $\displaystyle 6$ a.m., when will they ring together again ?
Find by prime factorisation the LCM of the numbers $\displaystyle 18180$ and 7575. Also, find the HCF of the two numbers.
Three bells ring at intervals of $\displaystyle 6$, $\displaystyle 12$ and $\displaystyle 18$ minutes. If all the three bells rang at $\displaystyle 6$ a.m., when will they ring together again ?
Marking-scheme solution
\[\begin{aligned}
& 18180=2^{2} \times 3^{2} \times 5 \times 101 \\
& 7575=3 \times 5^{2} \times 101 \\
& L C M=2^{2} \times 3^{2} \times 5^{2} \times 101=90900 \\
& H C F=3 \times 5 \times 101=1515
\end{aligned}
\]
LCM of $\displaystyle 6$, $\displaystyle 12$, $\displaystyle 18$ = $\displaystyle 36$
So, all the three bells ring together after $\displaystyle 36$ minutes at $\displaystyle 6$ : $\displaystyle 36$ AM
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CBSE Class 10 Mathematics past-paper question from the 2023board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.