Write the multiples of 6 that are greater than 20 but less than 50. Write all the multiples of 17 that are less than 80. Write all the multiples of 19 that are two-digit numbers. Find the LCM of: (a) 5 and 10 (b) 5, 6 and 10 (c) 6 and 8
Answer (1)
Let's address each part of the question step-by-step:
Multiples of 6 that are greater than 20 but less than 50:
To find multiples of 6, we start with the smallest number greater than 20 that is a multiple of 6, which is 24.
Then continue adding 6 to each subsequent result until we reach a number less than 50.
The multiples of 6 in this range are: 24 , 30 , 36 , 42 , 48
Multiples of 17 that are less than 80:
Start with 17 (the smallest multiple of 17), and keep adding 17 until reaching a number less than 80.
The multiples of 17 in this range are: 17 , 34 , 51 , 68
Multiples of 19 that are two-digit numbers:
The smallest two-digit multiple of 19 is 19 itself, and the largest is the highest multiple of 19 less than 100.
We identify these by continuing to add 19 until we exceed two digits.
The two-digit multiples of 19 are: 19 , 38 , 57 , 76 , 95
LCM (Least Common Multiple):
(a) LCM of 5 and 10:
Since 10 is a multiple of 5, the LCM is 10 itself.
(b) LCM of 5, 6, and 10:
List the multiples of each and find the smallest common multiple.
Multiples of 5: 5 , 10 , 15 , 20 , 25 , 30 , 35 , 40 , 45 , 50 , …
Multiples of 6: 6 , 12 , 18 , 24 , 30 , …
Multiples of 10: 10 , 20 , 30 , 40 , …
The smallest common multiple is 30. So, L CM ( 5 , 6 , 10 ) = 30 .
(c) LCM of 6 and 8:
Multiples of 6: 6 , 12 , 18 , 24 , 30 , 36 , 42 , 48 , …
Multiples of 8: 8 , 16 , 24 , 32 , 40 , 48 , …
The smallest common multiple is 24. So, L CM ( 6 , 8 ) = 24 .
These steps provide a clear and systematic way to determine the multiples and the least common multiples as required by the question.
