In a colony of 100 blocks of flats numbering 1 to 100 a school van stops at every sixth block while a school bus stops at every tenth block. On which stops will both of them stop if they start from the entrance of the colony
Answers
Step-by-step explanation:
A school van stops at every sixth block and a school bus stops at every tenth block. We have to find the common stops at which they both stop if they start from a same entrance. The LCM of 6 and 10 is 2 × 3 × 5 = 30. Firstly both will stop at 30th block, then 60th block and lastly at 90th block
Given : In a colony of 100 blocks of flats numbering 1 to 100
a school van stops at every sixth block while a school bus stops at every tenth block.
To Find : On which stops will both of them stop if they start from the entrance of the colony
Solution:
they start from the entrance of the colony Hence Block 0 or before Block 1.
school van stops at every sixth block
school bus stops at every tenth block.
To Find the stops where both stops we need to find LCM of 6 and 10 , and multiplies of LCM
6 = 2 * 3
10 = 2 * 5
LCM = 2 * 3 * 5 = 30
LCM ( 6 , 10) = 30
Multiples of 30 are 30 , 60 , 90 , 120 and so on
Hence Both stops at 30 , 60 and 90 blocks as 120 > 100 and there are only 100 Blocks
Hence both of them stop at 30th , 60th and 90th blocks
Additional Info:
LCM - Least common multiplier of given numbers is the least number which is perfectly divisible by given numbers.
LCM = product of each factor of highest power
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