ページ3:

b) The LCM of 15 and 25 is
15 25
3/3
LCM = 5×3×5
5
51
5
1
1
C) The LCM of two numbers is the smallest
number that is exactly divisible by both.
True/False?
True. 4
6
Multiple 44,8,12,16,.
Multiple 6:
6.12,18
So LCM of 4 and 6
9
is 12

ページ4:

d) The HCF of two numbers is the
largest number that divides both exactly
True/False?
True
HCF: Highest Common Factor
e) The LCM of 4 and 5 is 20
24
5
LCM 2x2x5
20
22
5
=
OY: 4×5
20
5| 1
5
1 1
f) The HCF of 12 and 18 is
Factor 12 : 1.2.3.4.16/11
9
Factor 18: 1, 2, 3, 6, 9, 18
HCF of 12 and 18 is b
6

ページ5:

g) The LCM of 7 and 10 is 70
LCM of 7 and 10 is 70
h) The HCF of 28 and 35 is 7
Factor 28 1,2,4,14,28
Factor 35: 1957 35
HCF of 28 and 35 is 7
i) The LCM of 8 and 12 is 24
28
12
LCM of 8 and 12
24
6
22
3
3| 1
3
= 2×2×2×3
=
- 24
1
1

ページ6:

j) The HCF of 45 and 60 is 15.
Factor 45: 1, 3, 5, 9, 13, 1545
9
Factor 60: 1, 2, 3, 5, 6, 10, 12 15, 30, 60
HCF of 45 and 60 is 15
2. Solve the following:
a) Find the LCM of 18 and 24.
2/18
24
3| 9
12
LCM of 18 and 24 is
3
3
4
2×3×3×4
=
72
4| 7
1
1
4
18
72

ページ7:

b) Find the HCF of 56 and 98 using
prime factorization.
prime factorization
Example: 2,3,5,7, 11,....
12 = 2x6
= 2 x2x3
• Prime factorization of 12
18 = 2x9
= 2×3×3
=
2×2×3
= 22×3
.: Prime factorization of 18: 2×3×3 = 2×3²
Prime factorization 56
Prime factorization 98
56 = 2×28
= 2×2×14
98 = 2x49
= 2×2×2×7
=25×7
3
=2×7×7
=2×72
HCF of 56 and 98 : 2x7
=
14

ページ8:

C) Find the LCM of 9, 12 and 15
39 12 15
345
LCM of 9, 12, 15 = 3×3×4×5
= 180
d) Find the HCF of
36 and 60 using
divison
method
30
1
Step 1 #
so
18|30
36 18
เศษ
18
12 × 2
=
(24)
1
Step2 # 36
24
2/22/2
24136
24
12
Step 3#
24
12
=
2
เศษ O
=
= 2
HCF of 36 and 60

ページ9:

e) If the LCM of two number is 80 and
their HCF is 15, find the product of the
two numbers.
Product of Two numbers = (HCF of the two numbers)
X (LCM of the two numbers).
A× B = H.C.F(A,F) × L.C.M (A, B)
Product of Two numbers = HCF × LCM
= 15×80
= 12.00

ページ10:

f) Find the LCM of 7, 14 and 28
7/7 14
28
1 2 4
LCM of 7, 14, 28
= 7×2×4
=
56
division
g)
Find the HCF of 45 and 75 using
method.
Step 1# 75
45
=
1 เศษ 36
step 2#
45
30
Step 3#
Glw CLA A
30
15
ย
1 เศษ 15
2

ページ11:

EX ของ
297 LCM 909 16,20 LINE 40 Using prime
factorization
16 = 2x8 = 2×2×2×2 = 2
20 = 5×4 = 5×2×2
40 = 4×10 = 2×2×2×5
: LCM = 5×24
=
28
=
5×22
5×23
=
= 5x2x2x2x2
= 80
(i) Find the HCF of 72 and 108
Using prime factorization.
72
=
8x9
108 = 9×12
HCF
=
2
=
=
2 x 3²
ง
3
2×2×2×3×3 = 2°×3²
2×3×2×3×3 = 22×33
=
(2x2)x(3×3)
4 x 9
=
= 36

ページ12:

h) Find the LCM of 12, 15, and 20 using
prime factorization
Prime factorization 12: 3×4 = 3×2×2 = 3×2°
2
Prime factorization 15
3×5
Prime factorization 20 = 2×2×5 = 5×2²
2
LCM: 2 × 3 × 5 = 60
EX 1 LCM ของ 18, 24 และ 30 Using prime
factorization
18
=
= 2 × 9
= 2×3×3 =
2x3²
2
24 = 2×12 = 2x4x3 = 2×2×2×3 = 3×2³
30 = 3×10
0018
0 18 = 2×3
2
=
24=3x23
30 = 3×2×5
3×2×5
พิจารณากำลังสุดของ และจำนวนเฉพาะ
32x2³×5
=360

ページ13:

(j) Find the LCM of 18 and 30 using
any
method
You prefer.
2
=
18 2 × 3 × 3
= 2×3²
30 = 2 × 3 ×5 = 2×3×S
LCM
=
2×3×5 = 2x9x5
= 90
ห.ร.ม. (HUF) - เรื่อง ตัวประกอบที่เหมือนกัน
และเลาะก้นั่งที่น้อยกว่า
ค.ร.น. (LC) - เลือก ตัวประกอบทุกตัว
ที่ปรากฏ และเลือกเลา กำลัง
สาระคณิต
ที่มากที่สุด

ページ14:

Factors, HCF and LCM
1: List all the factors of the following
number:
a) 60
b)80
16
1,2,3 4, 5, 6, 10, 12, 15, 20,30 60 1,2,4,5,8,10,20,4080
C) 75
1.3.5.15.25.25
0163
1.3.7.9.21,43
2: Express as a product of prime factors:
a) 99
b) 96
2x2x2x2x2x3
3x3x11
d) 36
c) 78
2×3×13
2×2×3×3

ページ15:

Numbers
Repeated Division
HCF
LCM
0 45
45 60
and
59 12
5x3=15
5x3 15 5x3×3×4
60
3|3 4
= 180
2
24
24 30
2×3×4×5
and
212
15
2×3=6
= 120
30
3 | 4
5
(3) 35
135 50
and
(57 10
5
50
=
5×7×10
350
4) 35
36 42
and
6
66
7
42
6×6×7
= 252
60
16072
12×5×6
12
and
12 56
=
360
72