HCF and LCM using prime factorisation

Step 1: (49=7^2) and (70=2\times5\times7). Step 2: For LCM, take (2), (5), and the higher power (7^2). Step 3: (2\times5\times49=490), so the answer is (490).

Step 1: (64=2^6) and (80=2^4\times5). Step 2: The common prime factor is (2), and the smaller power is (2^4). Step 3: (2^4=16), so the HCF is (16).

Step 1: (64=2^6) and (80=2^4\times5). Step 2: The highest powers are (2^6) and (5). Step 3: (64\times5=320), so the LCM is (320).

Step 1: (15=3\times5), (25=5^2), and (35=5\times7). Step 2: The common prime factor in all three numbers is (5). Step 3: Therefore, the HCF is (5).

Step 1: (15=3\times5), (25=5^2), and (35=5\times7). Step 2: The highest powers are (3), (5^2), and (7). Step 3: (3\times25\times7=525), so the LCM is (525).

Step 1: (18=2\times3^2), (27=3^3), and (45=3^2\times5). Step 2: The common prime factor is (3), and the smallest power is (3^2). Step 3: (3^2=9), so the answer is (9).

Step 1: (18=2\times3^2), (27=3^3), and (45=3^2\times5). Step 2: The highest powers are (2), (3^3), and (5). Step 3: (2\times27\times5=270), so the LCM is (270).

Step 1: The common prime factors are (2) and (3). Step 2: The smaller powers are (2^2) and (3). Step 3: (2^2\times3=12), so the HCF is (12).

Step 1: For LCM, take the highest powers of all prime factors. Step 2: The highest powers are (2^3), (3^2), and (5). Step 3: (8\times9\times5=360), so the answer is (360).

Step 1: The common prime factors are (2) and (3). Step 2: The smaller powers are (2^2) and (3). Step 3: (2^2\times3=12), so the HCF is (12).

Step 1: For LCM, choose the highest powers. Step 2: The highest powers are (2^4), (3), and (7). Step 3: (16\times3\times7=336), so the LCM is (336).

Step 1: For two numbers, product (=) HCF (\times) LCM. Step 2: (8\times96=768). Step 3: In such questions, apply the relation first and then multiply carefully.

Step 1: To find the product, multiply the HCF and LCM. Step 2: (15\times210=3150). Step 3: Use this relation directly for two numbers.

Step 1: Use the relation product (=) HCF (\times) LCM. Step 2: LCM (=\frac{1296}{18}=72). Step 3: After division, you can check by multiplying (18\times72).

Step 1: For two numbers, product (=) HCF (\times) LCM. Step 2: HCF (=\frac{1680}{280}=6). Step 3: It is important to place the given values correctly.

Step 1: For two numbers, HCF (\times) LCM equals the product of the two numbers. Step 2: (32\times72=2304). Step 3: In such questions, finding HCF and LCM separately is not necessary.

Step 1: (16=2^4) and (27=3^3). Step 2: They have no common prime factor. Step 3: So the HCF is (1), and these numbers are co-prime.

Step 1: (16=2^4) and (27=3^3). Step 2: There is no common factor, so the LCM is their product. Step 3: (16\times27=432), so the answer is (432).

Step 1: (9=3^2) and (20=2^2\times5). Step 2: They have no common prime factor. Step 3: The LCM of co-prime numbers is their product, so (9\times20=180).

Step 1: (26=2\times13) and (39=3\times13). Step 2: The common prime factor is (13). Step 3: Therefore, the HCF is (13).