The three three boys step off together from the same place if their step measure 36 CM 48 cm and 54 CM at what distance from the starting point will they again step together
Answers
GIVEN
The three three boys step off together from the same place.
Their step measurements are:-
36cm,48cm &54cm.
TO FIND
At what distance they will meet again
SOLUTION
CONCEPT OF LCM
It is the fundamental concept in mathematics. LCM means Lowest Common Multiple. That is in case of any 2 or more than 2 real number we can find their common multiple from which the given numbers can be divided leading remainder as zero.
*LCM can be calculated by Prime Factorisation Method.
Like A = c × d × e
B = f × d × g
LCM(A and B) = c × d × e × f × g
*multiply only factors of highest degree which are in common
ANSWER
We can find the minimum distance at which 3 of the boys will keep their foot together by LCM,
Lets prime factorise,
36 = 2 × 2 × 3 × 3 = 2^2 × 3^2
48 = 2 × 2 × 2 × 2 × 3 = 2^4 × 3
54 = 2 × 3 × 3 × 3 = 2 × 3^3
LCM(54,48,36) = 3^3 × 2^4 = 27×16= 432
Hence they will meet after 432cm =4.32m (ANS)