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# Find the HCF of the given problems106,159 and 265136,170 and 255100,140 and 315I'll mark you as the brainliest if it is a proper ans and it should be correct

The relation between the LCM and HCF of 106, 159 and 265 is given as, HCF(106, 159, 265) = [(106 × 159 × 265) × LCM(106, 159, 265)]/[LCM(106, 159) × LCM (159, 265) × LCM(106, 265)]

⇒ Prime factorization of 106, 159 and 265:

106 = 2 × 53

159 = 3 × 53

265 = 5 × 53

∴ LCM of (106, 159), (159, 265), (106, 265), and (106, 159, 265) is 318, 795, 530, and 1590 respectively.

Now, LHS = HCF(106, 159, 265) = 53.

And, RHS = [(106 × 159 × 265) × LCM(106, 159, 265)]/[LCM(106, 159) × LCM (159, 265) × LCM(106, 265)] = [(4466310) × 1590]/[318 × 795 × 530]

LHS = RHS = 53.

Hence verified.

Example 2: Find the highest number that divides 106, 159, and 265 completely.

Solution:

The highest number that divides 106, 159, and 265 exactly is their highest common factor.

Factors of 106 = 1, 2, 53, 106

Factors of 159 = 1, 3, 53, 159

Factors of 265 = 1, 5, 53, 265

The HCF of 106, 159, and 265 is 53.

∴ The highest number that divides 106, 159, and 265 is 53.

Example 3: Calculate the HCF of 106, 159, and 265 using LCM of the given numbers.

Solution:

Prime factorization of 106, 159 and 265 is given as,

106 = 2 × 53

159 = 3 × 53

265 = 5 × 53

LCM(106, 159) = 318, LCM(159, 265) = 795, LCM(265, 106) = 530, LCM(106, 159, 265) = 1590

⇒ HCF(106, 159, 265) = [(106 × 159 × 265) × LCM(106, 159, 265)]/[LCM(106, 159) × LCM (159, 265) × LCM(265, 106)]

⇒ HCF(106, 159, 265) = (4466310 × 1590)/(318 × 795 × 530)

⇒ HCF(106, 159, 265) = 53.

Therefore, the HCF of 106, 159 and 265 is 53.

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