Page 12 - 新思维数学活动用书7 样章

1.3 Lowest common multiples

Practice

7 Show that the multiples of 3 and 5 are multiples of 15.
8 Find the lowest common multiple of 6 and 14.
9 a Find the lowest common multiple of:

i 7 and 2 ii 7 and 4 iii 7 and 6
b Is there an easy method to find the lowest common multiple of 7 and a number less than 7?

c Does the method in part b work for 7 and a number more than 7?
10 Look at these numbers: 90 92 94 96 98 100
a i Which number is a multiple of 9 and 10?
ii Is this number the lowest common multiple?
b i Which number is a multiple of 2 and 7?

ii Is this number the lowest common multiple?
c i Which number is a multiple of 12 and 8?
ii Is this number the lowest common multiple?

11 Work out the lowest common multiple (LCM) of 2, 5 and 6.

Challenge
12 Find the LCM of 3, 8 and 9.
13 24 × 4 = 96

a Explain why 96 is a common multiple of 4 and 24.
b Is 96 the lowest common multiple of 4 and 24? Give evidence to justify your answer.
14 Two numbers have a LCM of 45. The two numbers add up to 14. Find the two numbers.

15 The LCM of two numbers is 63. Work out the two numbers.

11