$12= 2 \times 2 \times 3$
$16 = 2 \times 2 \times 2 \times 2$
$24 = 2 \times 2 \times 2 \times 3$
$36= 2 \times 2 \times 3 \times 3$
LCM = $2 \times 2 \times 2 \times 2 \times 3 \times 3 =144$
$70 = 2 \times 5 \times 7$
$105 = 3 \times 7 \times 5$
$175 = 5 \times 5 \times 7$
HCF =$5 \times 7 =35$
Two prime numbers whose difference is 2 are called twin primes.
For example:
3 and 5 are twin primes
5 and 7 are twin primes
A prime triplet is a set of three prime numbers of the form:
(p,p+2,p+6) or (p,p+4,p+6)
Some Examples are (5, 7, 11), (7, 11, 13), (11, 13, 17)
$1350 = 2 \times 3 \times 3 \times 3 \times 5 \times 5$
Prime factors in descending order
5 > 3 >2
a. 44
b. 125
c. 48
d. 64
53 = 13 + 17 + 23
or 53 = 7 + 17 + 29
We have to find the LCM of 80 cm, 85 cm and 90 cm
LCM =12240 cm
LCM of 12,16,24 and 36 =144
Least Number = 144 + 7 = 151
Multiples of 11 = 11,22,33,44,55,66,77,88
So multiples greater than 56 but less than 79 are 66 and 77
1.
a.
11= 11
44 =11 X 2 X 2
HCF =11
b.
35 = 5 x 7
42 = 7 x 3 x 2
HCF =7
c.
128= 2 x 2 x 2 x 2 x 2 x 2 x 2
60 = 2 x 2 x 3 x 5
HCF =4
d. 81 = 3 x 3 x3 x3
63 = 7 x 3 x 3
HCF =9
e.
36 =2 x 2 x3 x3
180 = 2 x 2 x 5 x 3 x 3
HCF = 12
f.
1152=2 x 2 x 2 x 2 x 2 x 2 x 2 x3 x3
1664=2 x 2 x 2 x 2 x 2 x 2 x 2 x 13
HCF= 128
g.
70 =2 x 5 x 3 x 3
115= 23 x 5
175 = 5 x 5 x7
HCF = 5
h.7
i. 9
j. 1
a.
$4=2 \times 2$
$7= 7 \times 1$
$12 =2 \times 2 \times 3$
$84= 2 \times 2 \times 3 \times 7$
LCM =$2 \times 2 \times 3 \times 7 =84$
b.
$25 = 5 \times 5$
$15 = 5 \times 3$
$36 = 2 \times 2 \times 3 \times 3$
LCM =$2 \times 2 \times 3 \times 3 \times 5 \times 5 =900$
c.
$24=2 \times 2 \times 2 \times 3$
$36= 2 \times 2 \times 3 \times 3$
$40= 2 \times 2 \times 2 \times 5$
LCM =$2 \times 2 \times 2 \times 3 \times 3 \times 5= 360$
d.
$27 = 3 \times 3 \times 3$
$36=2 \times 2 \times 3 \times 3$
LCM =$2 \times 2 \times 3 \times 3 \times 3 = 108$
e. 72
f. 420
a.
$9=3 \times 3$
$12 =2 \times 2 \times 3$
HCF =3
b.
$10=2 \times 5$
$11 =1 \times 11$
LCM =110
c.
$4=2 \times 2$
$13 =1 \times 13$
LCM =52
d.
$6=2 \times 3$
$16 =2 \times 2 \times 2 \times 2$
HCF =2
e.
$17=1 \times 17$
$15 =3 \times 5$
LCM =255
f.
$6=2 \times 3$
$22 =2 \times 11$
HCF =2
g.
$5=5 \times 1$
$20 =2 \times 2 \times 5$
LCM =20
h.
$22=2 \times 11$
$66 =3 \times 2 \times 11$
HCF =22
i.
$8=2 \times 2 \times 2$
$16 =2 \times 2 \times 2 \times 2$
HCF =8
j.
$2=2$
$132 =2 \times 2 \times 3 \times 11$
HCF =2
k.
$30=2 \times 3 \times 5$
$6=2 \times 3$
LCM =30
k.
$25=5 \times 5$
$32 =2 \times 2 \times 2 \times 2 \times 2$
LCM =800