Question

find the LCM and HCF of the 26 and 91 pairs of intigers and verify that LCM ×HCF=,product of the two no. ​

Answer 1

Answer:

LCM(26,91) = 182. HCF = 13

Step-by-step explanation:

Prime Factorization of 26 = 2^1 * 13^1

Prime Factorization of 91 = 7^1 * 13^1

Now multiplying the highest exponent prime factors to calculate the LCM of 26 and 91.

LCM(26,91) = 2^1 × 13^1 × 7^1

LCM(26,91) = 182

HCF(GCF):

Find the prime factorization of 26

26 = 2 × 13

Find the prime factorization of 91

91 = 7 × 13

To find the gcf, multiply all the prime factors common to both numbers:

Therefore, GCF = 13

= 182 * 13 = 182 * 13

= 2366 = 2366

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Answer 2

⠀⠀⠀⠀ $\pink{\boxed{\sf{\blue{\:SoLution...}}}}$⠀

⠀⠀⠀⠀ ⠀ ⠀⠀ ⠀⠀⠀

❐⠀factors of 91 = 13 × 7

❐⠀factors of 26 = 2 × 13

⠀⠀⠀⠀ ⠀ ⠀⠀ ⠀⠀⠀

---✁ ⠀$\red{\boxed{\sf{\green{\:H.C.F.\:=\:13...}}}}$⠀⠀

⠀⠀⠀⠀ ⠀ ⠀⠀ ⠀⠀⠀

⠀We know that...

Product of two numbers = H.C.F. × L.C.M.⠀

⠀⠀ ⠀ ⠀⠀ ⠀91 × 26 ⠀ =⠀13 × L.C.M.

⠀⠀⠀⠀ ⠀ ⠀ 91 × 26 / 13 = L.C.M.

⠀⠀⠀⠀ ⠀ ⠀⠀ ⠀⠀⠀

---✁ ⠀$\red{\boxed{\sf{\green{\:L.C.M.\:=\:182...}}}}$⠀⠀

⠀⠀⠀⠀ ⠀ ⠀⠀ ⠀⠀⠀

__________verification__________

⠀⠀⠀

⠀⠀⠀⠀ ⠀ ⠀91 × 26⠀ =⠀13 × 182

⠀⠀⠀⠀ ⠀ ⠀ 2,366⠀⠀= ⠀2,366

⠀⠀⠀⠀ ⠀ ⠀${\overbrace{\underbrace{\red{H.C.F.\:=\:L.C.M.}}}}$⠀ ⠀⠀⠀

________hence verified_______⠀⠀⠀

⠀ ⠀⠀⠀