Question

Find the L.C.M. and H.C.F. of 260 and 120and verify that LCM × HCF = product of the two numbers.

Answer 1

AnsWer :

31200.

SolutioN :

Let,

• The number be N1 = 260.
• Other number be 120.

N1

2 | 260

5 | 1 30

2 | 26

13 | 13

| 1

___________

For N2.

2 | 120

2 | 60

2 | 30

3 | 10

5 | 5

| 1

* LCM ( N1 , N2 ) →

• 2 * 2 * 5 * 13 → 2² * 5 * 13.
• 2 * 2 * 2 * 3 * 5. → 2³ * 3 * 5.

→ 2³ * 3 * 5 * 13.

→ 8 * 3 * 5 * 13

→ 1560.

____________________

* HCF ( N1 , N2 ) →

• 2 * 2 * 5 * 13 → 2² * 5 * 13.
• 2 * 2 * 2 * 3 * 5. → 2³ * 3 * 5.

→ 2² * 5

→ 4 * 5

→ 20.

Now, Product of HCF * LCM

→ 1560 * 20

→ 31200.

________________________

Let's find product of N1 and N2.

→ N1 * N2 → 120 * 260.

→ 31200.

__________

Now, We know.

$\tt \dagger \: \: \: \: \: HCF \times LCM = Product \: of \: two \: number.$

$\tt : \implies 20 \times 1560 = N1 \times N2.$

$\tt : \implies 31200 = 120 \times 260$

$\tt : \implies 31200 = 31200.$

Hence Verify.

Answer 2

Step-by-step explanation:

QUESTION:-

Find the L.C.M. and H.C.F. of 260 and 120and verify that LCM × HCF = product of the two numbers.

ANSWER :-

Let,

The number be N1 = 260.

Other number be 120.

N1

2 | 260

5 | 1 30

2 | 26

13 | 13

| 1

___________

For N2.

2 | 120

2 | 60

2 | 30

3 | 10

5 | 5

| 1

* LCM ( N1 , N2 ) →

2 * 2 * 5 * 13 → 2² * 5 * 13.

2 * 2 * 2 * 3 * 5. → 2³ * 3 * 5.

→ 2³ * 3 * 5 * 13.

→ 8 * 3 * 5 * 13

→ 1560.

___________________

* HCF ( N1 , N2 )

2 * 2 * 5 * 13 → 2² * 5 * 13.

2 * 2 * 2 * 3 * 5. → 2³ * 3 * 5.

→ 2² * 5

→ 4 * 5

→ 20.

Now, Product of HCF * LCM

→ 1560 * 20

→ 31200.

________________________

Let's find product of N1 and N2.

→ N1 * N2 → 120 * 260.

→ 31200.

__________