Download 3 - NCETM

Least Common Multiple
Using Factor Trees to find the
least common multiple (LCM)
Least Common Multiple
• The least common multiple of two (or
more) numbers is the smallest number
that can be divided by both (or all) the
numbers.
• Example the LCM of 4 and 7 is 4x7 = 28
Finding the LCM
• To find the LCM we can list all the
multiples of each number and find the first
one that appears in each list
• Eg LCM 24 and 36
• 24, 48, 72, 96, 120 . . .
• 36, 72, 108, 144 . . .
• So the LCM of 24 and 36 is 72
But, if you have big/nasty numbers
• This is takes ages
• Easy to make a mistake
LCM – Using Factor Trees
Find the LCM of 45 and 72
1. First write each number as a product of
its primes
2. Find the Highest Common Factor by
identifying the primes which appear in
both numbers
3. Find the Lowest Common Multiple by
multiplying the Highest Common Factor
by all the factors that are leftover.
HELP!!
1. Product of Primes
• 45
• 72
72
45
2
5
36
9
2
3
3
2
3 x 3 x 5 = 45
32 x 5 = 45
18
2 x 2 x 2 x 3 x 3 = 72
23 x 32 = 72
9
3
3
2. Highest Common Factor
• 45
• 72
72
45
2
5
36
9
2
3
18
3
2
HCF = 3 x 3 = 9
9
3
3
3. LCM = HCF x Leftovers
• 45
• 72
45
72
5
9
2
3
3
HCF = 3 x 3 = 9
Leftovers = 5 x 23 = 40
LCM = 9 x 40 = 360
36
2
2
18
9
3
3
Find the HCF and then LCM of the
following:
1.
2.
3.
4.
5.
6.
7.
8.
18 and 30
27 and 36
14 and 35
15 and 55
24 and 56
35 and 42
56 and 100
108 and 126
=
=
=
=
=
=
=
=
90
108
70
165
168
210
1400
756