Application Problems on HCF and LCM

Find the smallest number that can be divided by $254$ and $508$ which leaves the remainder $4$.

Find the ratio of the HCF and the LCM of the numbers 18 and 30 .

A book seller has $175$ English books, $245$ Science books and $385$ Mathematics books. He wants to sell the books in a box, subject-wise in equal numbers. What will be the greatest number of the boxes required? Also find the number of books for each subject in a box.

What is the greatest number that will divide $62,78$ and $109$ leaving remainders $2,3$ and $4$ respectively?

There are four Mobile Phones in a house. At $5 \mathrm{a}.\mathrm{m}$, all the four Mobile Phones will ring together. Thereafter, the first one rings every $15$ minutes, the second one rings every $20$ minutes, the third one rings every $25$ minutes and the fourth one rings every $30$ minutes. At what time, will the four Mobile Phones ring together again?

What is the greatest possible volume of a vessel that can be used to measure exactly the volume of milk in cans (in full capacity) of $80 \mathrm{litres}, 100 \mathrm{litres}$ and $120 \mathrm{litres}$?

Find the HCF and the LCM of the numbers $154, 198$ and $286$.

Wilson, Mathan and Guna can complete one round of a circular track in $10,15$ and $20$ minutes respectively. If they start together at $7 \mathrm{a}.\mathrm{m}.$ from the starting point, at what time will they meet together again at the starting point?

Malarvizhi, Karthiga and Anjali are friends and natives of the same village. They work at different places. Malarvizhi comes to her home once in $5$ days. Similarly,Karthiga and Anjali come to their homes once in $6$ days and $10$ days respectively. Assuming that they met each other on the $1^{\text{st }}$ of October, and met again on $k^{st}$ October. Find the value of $k$.

Find the smallest number which is exactly divisible by all the numbers from $1$ to $9$.

Find the length of the longest rope that can be used to measure exactly the ropes of length $1 \mathrm{m} 20 \mathrm{cm},3 \mathrm{m} 60 \mathrm{cm}$ and $4 \mathrm{m}$.

The LCM of two numbers is $210$ and their HCF is $14$. How many such pairs are possible?

The traffic lights at three different road junctions change after every $40$ Seconds, $60$ Seconds and $72$ Seconds respectively. If they changed simultaneously together at $8 \mathrm{a}.\mathrm{m}$ at the junctions, at what time will they simultaneously change together again?

Find the LCM of given set of numbers using prime factorisation method.

$15, 25, 75$

Find the LCM of given set of numbers using prime factorisation method:

$30, 40, 60$

Find the LCM of given set of numbers using prime factorisation method:

$14,42$

Find the LCM of given numbers using the prime factorization method.

$10,15$

Find the LCM of given set of numbers using prime factorisation method:

$8, 12$

Find the LCM of given set of numbers using the prime factorization method:

$6, 9$

Find the HCF of the set of numbers $45,55,95$.