Question

Three bells toll at intervals of 12, 18, 20 minutes respectively. If they start tolling
together, after what time will they next toll together?​

Answer 1

Step-by-step explanation:

hi

Answer. Lcm=180 therefore they will ring again at the same time together after 180 minutes which is 3 hours.

here's is your answer hope it helps

:))

Answer 2

Basic Concept Used :-

Three bells tolls at intervals of every 12 minutes, 18 minutes and 20 minutes respectively.

So, the time, they toll together is equals to LCM (12, 18, 20)

Let's solve the problem now!!!

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

Consider,

$\red{\bf :\longmapsto\:Prime \: factorization \: of \: 12}$

$\begin{gathered}\begin{gathered}\begin{gathered} \:\: \begin{array}{c|c} {\underline{\sf{2}}}&{\underline{\sf{\:\:12\:\:\:}}}\\ {\underline{\sf{2}}}& \underline{\sf{\: \: 6\: \:\:}} \\ {\underline{\sf{3}}}& \underline{\sf{\: \: 3\: \:\:}} \\{\sf{}}&\underline{\sf{\:\:1 \:\:}}\end{array}\end{gathered}\end{gathered}\end{gathered}$

$\red{\bf :\longmapsto\:Prime \: factorization \: of \: 12 = {2}^{2} \times 3 }$

Consider,

$\green{\bf :\longmapsto\:Prime \: factorization \: of \: 18}$

$\begin{gathered}\begin{gathered}\begin{gathered} \:\: \begin{array}{c|c} {\underline{\sf{2}}}&{\underline{\sf{\:\:18\:\:\:}}}\\ {\underline{\sf{3}}}& \underline{\sf{\: \: 9\: \:\:}} \\ {\underline{\sf{3}}}& \underline{\sf{\: \: 3\: \:\:}} \\{\sf{}}&\underline{\sf{\:\:1 \:\:}}\end{array}\end{gathered}\end{gathered}\end{gathered}$

$\green{\bf :\longmapsto\:Prime \: factorization \: of \: 18 = 2 \times {3}^{2} }$

Consider,

$\blue{\bf :\longmapsto\:Prime \: factorization \: of \: 20}$

$\begin{gathered}\begin{gathered}\begin{gathered} \:\: \begin{array}{c|c} {\underline{\sf{2}}}&{\underline{\sf{\:\:20\:\:\:}}}\\ {\underline{\sf{2}}}& \underline{\sf{\: \: 10\: \:\:}} \\ {\underline{\sf{5}}}& \underline{\sf{\: \: 5\: \:\:}} \\{\sf{}}&\underline{\sf{\:\:1 \:\:}}\end{array}\end{gathered}\end{gathered}\end{gathered}$

$\blue{\bf :\longmapsto\:Prime \: factorization \: of \: 20 = {2}^{2} \times 5}$

Thus,

$\pink{\rm :\longmapsto\:LCM(12, 18, 20) = {2}^{2} \times {3}^{2} \times 5 = 180}$

Hence,

• Three bells toll together after 180 minutes or 3 hours.

Additional Information :-

If a and b are two natural numbers, then

• HCF × LCM = a × b

• HCF < or = (a, b)

• LCM > or = (a, b)

• HCF is a factor of LCM