1. Find the smallest number which when divided by 21, 45 and 36 will leave a remainder of 7 in each case.
We need to find the least common multiple of these numbers and then 7 to it so that there is a remainder of 7 when we divide by these numbers.
If we divide 1260 by 21, 45 and 36 we will not get a reminder. In order to have reminder of 7, we need to add 7 to the LCM. That is 1260+7 = 1267
Answer: The smallest number when divided by 21, 36 and 45 that will leave a reminder of 7 is 1267.
RELATIONSHIP BETWEEN HCF AND LCM
Find the HCF and LCM of 15 and 9.
15 = 3×5
9 = 3×3
HCF = 3and LCM = 3×3×5 = 45
Multiply the HCF and LCM
45×3 = 135
Multiply the two numbers
15×9 = 135
The product of two numbers is equal to the product of their HCF and LCM.
You can use this relationship to find the numbers when you know their HCF and LCM.
Two numbers have their HCF as 4 and their LCM as 48. If one of the numbers is 16, find the other number.
HCF×LCM = Given number × the other number
HCF × LCM = the product of the numbers
4×48 = 192
16×? = 192
Divide to find out.
192÷16 = 12
Answer: The other number is 12.